(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 565640, 12207] NotebookOptionsPosition[ 548454, 11659] NotebookOutlinePosition[ 553250, 11791] CellTagsIndexPosition[ 551974, 11759] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["BinaryTrees 1.03", "Title"], Cell["documentation notebook", "Subtitle"], Cell[TextData[{ "Eric Rowland\n", ButtonBox["http://math.tulane.edu/~erowland/packages.html", BaseStyle->"Hyperlink", ButtonData:>{ URL["http://math.tulane.edu/~erowland/packages.html"], None}] }], "Subsubtitle"], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell["\<\ BinaryTrees is a package for generating, visualizing, and manipulating binary \ trees. This introduction gets you started with a few features of the package; the \ next section provides a complete list of package symbols along with their \ usage messages and further examples.\ \>", "Text"], Cell[TextData[{ "To use BinaryTrees, first you will need to load the package by evaluating \ the following cell. (If you need help, see ", ButtonBox["loading a package", BaseStyle->"Hyperlink", ButtonData->{ URL["http://math.tulane.edu/~erowland/packages/loadingapackage.html"], None}, ButtonNote-> "http://math.tulane.edu/~erowland/packages/loadingapackage.html"], ".)" }], "Text"], Cell[BoxData[ RowBox[{"<<", "BinaryTrees`"}]], "Code"], Cell[CellGroupData[{ Cell["Representing trees", "Subsection"], Cell["\<\ A rooted, ordered tree is represented by an expression in which each vertex \ corresponds to a list containing its children. For example, here is a 5-leaf \ binary tree:\ \>", "Text"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}]], "Input"], Cell[TextData[{ "The ", StyleBox["Mathematica", FontSlant->"Italic"], " symbol ", StyleBox["TreeForm", "Input"], " displays expressions graphically. ", StyleBox["BareTreeForm", "Input"], " uses ", StyleBox["TreeForm", "Input"], " to draw trees without vertex labels:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], "]"}]], "Input"], Cell[BoxData[ GraphicsBox[ TagBox[GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, { 1.2510864843424487`, 0.}, {2.0851441405707476`, 0.}, { 2.5021729686848975`, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, { 1.2510864843424487`, 0.}, {2.0851441405707476`, 0.}, { 2.5021729686848975`, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]]], "Output"] }, Open ]], Cell[TextData[{ StyleBox["BinaryTrees", "Input"], " gives a list of all binary trees with a fixed number of leaves." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"BinaryTrees", "[", "4", "]"}], "\[IndentingNewLine]", RowBox[{"BareTreeForm", "/@", "%"}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}]], "Output"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {1.3416407864998738`, 0.894427190999916}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 2.6832815729997477`}, { 0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {1.3416407864998738`, 0.894427190999916}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.894427190999916}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 7}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 2.6832815729997477`}, { 0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.894427190999916}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2247448713915892`, 1.6329931618554523`}, { 0.4082482904638631, 0.8164965809277261}, {0., 0.}, { 0.8164965809277261, 0.}, {2.041241452319315, 0.8164965809277261}, { 1.6329931618554523`, 0.}, {2.4494897427831783`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2247448713915892`, 1.6329931618554523`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4082482904638631, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.041241452319315, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6329931618554523`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.4494897427831783`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2247448713915892`, 1.6329931618554523`}, { 0.4082482904638631, 0.8164965809277261}, {0., 0.}, {0.8164965809277261, 0.}, {2.041241452319315, 0.8164965809277261}, {1.6329931618554523`, 0.}, {2.4494897427831783`, 0.}}]& ], AspectRatio->NCache[Rational[1, 2] 3^Rational[1, 2], 0.8660254037844386], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.894427190999916}, { 0.8944271909999159, 0.894427190999916}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 4}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.894427190999916}, { 0.8944271909999159, 0.894427190999916}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.894427190999916}, {1.7888543819998317`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 6}, {3, 4}, {3, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.894427190999916}, {1.7888543819998317`, 1.788854381999832}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Trees", "Input"], " gives a list of all trees with a fixed number of vertices." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"Trees", "[", "4", "]"}], "\[IndentingNewLine]", RowBox[{"BareTreeForm", "/@", "%"}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"{", RowBox[{"{", "}"}], "}"}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"{", "}"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"{", "}"}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}]], "Output"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0., 3.}, {0., 2.}, {0., 1.}, {0., 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {3, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0., 3.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0., 3.}, {0., 2.}, {0., 1.}, {0., 0.}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4629100498862757, 1.8516401995451028`}, { 0.4629100498862757, 0.9258200997725514}, {0., 0.}, { 0.9258200997725514, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {2, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 1.8516401995451028`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4629100498862757, 1.8516401995451028`}, { 0.4629100498862757, 0.9258200997725514}, {0., 0.}, {0.9258200997725514, 0.}}]& ], AspectRatio->NCache[Rational[3, 2]^Rational[1, 2], 1.224744871391589], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4629100498862757, 1.8516401995451028`}, {0., 0.9258200997725514}, {0.9258200997725514, 0.9258200997725514}, { 0.9258200997725514, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 1.8516401995451028`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4629100498862757, 1.8516401995451028`}, { 0., 0.9258200997725514}, {0.9258200997725514, 0.9258200997725514}, { 0.9258200997725514, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4629100498862757, 1.8516401995451028`}, {0., 0.9258200997725514}, {0., 0.}, {0.9258200997725514, 0.9258200997725514}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 4}, {2, 3}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 1.8516401995451028`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.9258200997725514}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4629100498862757, 1.8516401995451028`}, { 0., 0.9258200997725514}, {0., 0.}, {0.9258200997725514, 0.9258200997725514}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.7745966692414834, 0.7745966692414834}, {0., 0.}, {0.7745966692414834, 0.}, {1.5491933384829668`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {1, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.7745966692414834, 0.7745966692414834}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7745966692414834, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.5491933384829668`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.7745966692414834, 0.7745966692414834}, {0., 0.}, {0.7745966692414834, 0.}, {1.5491933384829668`, 0.}}]& ], AspectRatio->NCache[Rational[2, 3]^Rational[1, 2], 0.816496580927726], FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "Rooted binary trees with ", Cell[BoxData[ FormBox["n", TraditionalForm]]], " leaves are in bijection to general rooted trees with ", Cell[BoxData[ FormBox["n", TraditionalForm]]], " vertices, via ", StyleBox["BinaryTree", "Input"], " and its inverse, ", StyleBox["FromBinaryTree", "Input"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"BareTreeForm", "/@", RowBox[{"BinaryTree", "/@", RowBox[{"Trees", "[", "4", "]"}]}]}], "\[IndentingNewLine]", RowBox[{"BareTreeForm", "/@", RowBox[{"FromBinaryTree", "/@", RowBox[{"BinaryTrees", "[", "4", "]"}]}]}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.894427190999916}, {1.7888543819998317`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 6}, {3, 4}, {3, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.894427190999916}, {1.7888543819998317`, 1.788854381999832}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.894427190999916}, { 0.8944271909999159, 0.894427190999916}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 4}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.894427190999916}, { 0.8944271909999159, 0.894427190999916}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.894427190999916}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 7}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 2.6832815729997477`}, { 0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.894427190999916}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2247448713915892`, 1.6329931618554523`}, { 0.4082482904638631, 0.8164965809277261}, {0., 0.}, { 0.8164965809277261, 0.}, {2.041241452319315, 0.8164965809277261}, { 1.6329931618554523`, 0.}, {2.4494897427831783`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2247448713915892`, 1.6329931618554523`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4082482904638631, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.041241452319315, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6329931618554523`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.4494897427831783`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2247448713915892`, 1.6329931618554523`}, { 0.4082482904638631, 0.8164965809277261}, {0., 0.}, {0.8164965809277261, 0.}, {2.041241452319315, 0.8164965809277261}, {1.6329931618554523`, 0.}, {2.4494897427831783`, 0.}}]& ], AspectRatio->NCache[Rational[1, 2] 3^Rational[1, 2], 0.8660254037844386], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {1.3416407864998738`, 0.894427190999916}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 2.6832815729997477`}, { 0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {1.3416407864998738`, 0.894427190999916}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.7745966692414834, 0.7745966692414834}, {0., 0.}, {0.7745966692414834, 0.}, {1.5491933384829668`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {1, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.7745966692414834, 0.7745966692414834}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7745966692414834, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.5491933384829668`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.7745966692414834, 0.7745966692414834}, {0., 0.}, {0.7745966692414834, 0.}, {1.5491933384829668`, 0.}}]& ], AspectRatio->NCache[Rational[2, 3]^Rational[1, 2], 0.816496580927726], FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4629100498862757, 1.8516401995451028`}, {0., 0.9258200997725514}, {0.9258200997725514, 0.9258200997725514}, { 0.9258200997725514, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 1.8516401995451028`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4629100498862757, 1.8516401995451028`}, { 0., 0.9258200997725514}, {0.9258200997725514, 0.9258200997725514}, { 0.9258200997725514, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4629100498862757, 1.8516401995451028`}, {0., 0.9258200997725514}, {0., 0.}, {0.9258200997725514, 0.9258200997725514}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 4}, {2, 3}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 1.8516401995451028`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.9258200997725514}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4629100498862757, 1.8516401995451028`}, { 0., 0.9258200997725514}, {0., 0.}, {0.9258200997725514, 0.9258200997725514}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4629100498862757, 1.8516401995451028`}, { 0.4629100498862757, 0.9258200997725514}, {0., 0.}, { 0.9258200997725514, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {2, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 1.8516401995451028`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4629100498862757, 1.8516401995451028`}, { 0.4629100498862757, 0.9258200997725514}, {0., 0.}, {0.9258200997725514, 0.}}]& ], AspectRatio->NCache[Rational[3, 2]^Rational[1, 2], 1.224744871391589], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0., 3.}, {0., 2.}, {0., 1.}, {0., 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {3, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0., 3.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0., 3.}, {0., 2.}, {0., 1.}, {0., 0.}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "Trees with ", Cell[BoxData[ FormBox["n", TraditionalForm]]], " vertices are also in bijection to Dyck words of length ", Cell[BoxData[ FormBox[ RowBox[{"2", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}], TraditionalForm]]], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"DyckWord", "/@", RowBox[{"Trees", "[", "4", "]"}]}], "\[IndentingNewLine]", RowBox[{"BareTreeForm", "/@", RowBox[{"FromDyckWord", "/@", RowBox[{"DyckWords", "[", "3", "]"}]}]}]}], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"\<\"000111\"\>", ",", "\<\"001011\"\>", ",", "\<\"010011\"\>", ",", "\<\"001101\"\>", ",", "\<\"010101\"\>"}], "}"}]], "Output"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.7745966692414834, 0.7745966692414834}, {0., 0.}, {0.7745966692414834, 0.}, {1.5491933384829668`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {1, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.7745966692414834, 0.7745966692414834}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7745966692414834, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.5491933384829668`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.7745966692414834, 0.7745966692414834}, {0., 0.}, {0.7745966692414834, 0.}, {1.5491933384829668`, 0.}}]& ], AspectRatio->NCache[Rational[2, 3]^Rational[1, 2], 0.816496580927726], FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4629100498862757, 1.8516401995451028`}, {0., 0.9258200997725514}, {0.9258200997725514, 0.9258200997725514}, { 0.9258200997725514, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 1.8516401995451028`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4629100498862757, 1.8516401995451028`}, { 0., 0.9258200997725514}, {0.9258200997725514, 0.9258200997725514}, { 0.9258200997725514, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4629100498862757, 1.8516401995451028`}, { 0.4629100498862757, 0.9258200997725514}, {0., 0.}, { 0.9258200997725514, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {2, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 1.8516401995451028`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4629100498862757, 1.8516401995451028`}, { 0.4629100498862757, 0.9258200997725514}, {0., 0.}, {0.9258200997725514, 0.}}]& ], AspectRatio->NCache[Rational[3, 2]^Rational[1, 2], 1.224744871391589], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0., 3.}, {0., 2.}, {0., 1.}, {0., 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {3, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0., 3.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0., 3.}, {0., 2.}, {0., 1.}, {0., 0.}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4629100498862757, 1.8516401995451028`}, {0., 0.9258200997725514}, {0., 0.}, {0.9258200997725514, 0.9258200997725514}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 4}, {2, 3}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4629100498862757, 1.8516401995451028`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9258200997725514}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9258200997725514, 0.9258200997725514}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4629100498862757, 1.8516401995451028`}, { 0., 0.9258200997725514}, {0., 0.}, {0.9258200997725514, 0.9258200997725514}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Families of trees", "Subsection"], Cell["Several particular families of trees are implemented.", "Text"], Cell[TextData[{ "A path tree is a binary tree in which at most one vertex on each level has \ children of its own. ", StyleBox["PathTrees", "Input"], " gives the ", Cell[BoxData[ FormBox["n", TraditionalForm]]], "-leaf path trees:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"PathTrees", "[", "6", "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 1.7888543819998317`, 1.788854381999832}, {1.3416407864998738`, 0.8944271909999162}, {2.23606797749979, 0.8944271909999162}, { 1.7888543819998317`, 0.}, {2.6832815729997477`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 1.7888543819998317`, 1.788854381999832}, {1.3416407864998738`, 0.8944271909999162}, {2.23606797749979, 0.8944271909999162}, { 1.7888543819998317`, 0.}, {2.6832815729997477`, 0.}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 1.7888543819998317`, 1.788854381999832}, {1.3416407864998738`, 0.8944271909999162}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {2.23606797749979, 0.8944271909999162}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 11}, {8, 9}, {8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999162}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 1.7888543819998317`, 1.788854381999832}, {1.3416407864998738`, 0.8944271909999162}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {2.23606797749979, 0.8944271909999162}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {1.3416407864998738`, 0.8944271909999162}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {1.7888543819998317`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 11}, {6, 7}, {6, 8}, {8, 9}, {8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {1.3416407864998738`, 0.8944271909999162}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {1.7888543819998317`, 1.788854381999832}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, { 1.7888543819998317`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 11}, {6, 7}, {6, 10}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, {1.7888543819998317`, 1.788854381999832}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {1.3416407864998738`, 0.8944271909999162}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.683281572999748}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 11}, {4, 5}, {4, 6}, {6, 7}, {6, 8}, {8, 9}, {8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {1.3416407864998738`, 0.8944271909999162}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.683281572999748}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999162}, {1.3416407864998738`, 2.683281572999748}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 11}, {4, 5}, {4, 6}, {6, 7}, {6, 10}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999162}, {1.3416407864998738`, 2.683281572999748}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.683281572999748}, { 0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, { 0.8944271909999159, 0.8944271909999162}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, { 1.7888543819998317`, 2.683281572999748}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 11}, {4, 5}, {4, 10}, {5, 6}, { 5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.683281572999748}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.683281572999748}, { 0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, { 0.8944271909999159, 0.8944271909999162}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, { 1.7888543819998317`, 2.683281572999748}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.683281572999748}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999162}, {1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.683281572999748}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 11}, {4, 5}, {4, 10}, {5, 6}, { 5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.683281572999748}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.683281572999748}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999162}, {1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.683281572999748}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {1.3416407864998738`, 1.788854381999832}, { 0.8944271909999159, 0.8944271909999162}, {1.7888543819998317`, 0.8944271909999162}, {1.3416407864998738`, 0.}, {2.23606797749979, 0.}, {1.3416407864998738`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, {6, 8}, {8, 9}, {8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {1.3416407864998738`, 1.788854381999832}, { 0.8944271909999159, 0.8944271909999162}, {1.7888543819998317`, 0.8944271909999162}, {1.3416407864998738`, 0.}, {2.23606797749979, 0.}, {1.3416407864998738`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {1.3416407864998738`, 1.788854381999832}, { 0.8944271909999159, 0.8944271909999162}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.7888543819998317`, 0.8944271909999162}, { 1.3416407864998738`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, {6, 10}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {1.3416407864998738`, 1.788854381999832}, { 0.8944271909999159, 0.8944271909999162}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.7888543819998317`, 0.8944271909999162}, { 1.3416407864998738`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, {0.8944271909999159, 0.8944271909999162}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, {1.3416407864998738`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 4}, {4, 5}, {4, 10}, {5, 6}, { 5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, {0.8944271909999159, 0.8944271909999162}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, {1.3416407864998738`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999162}, {1.7888543819998317`, 1.788854381999832}, {1.7888543819998317`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 4}, {4, 5}, {4, 10}, {5, 6}, { 5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999162}, {1.7888543819998317`, 1.788854381999832}, {1.7888543819998317`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, { 1.3416407864998738`, 0.8944271909999162}, {0.8944271909999159, 0.}, { 1.7888543819998317`, 0.}, {1.3416407864998738`, 2.683281572999748}, { 1.7888543819998317`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 10}, {3, 4}, {3, 5}, {5, 6}, { 5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, { 1.3416407864998738`, 0.8944271909999162}, {0.8944271909999159, 0.}, { 1.7888543819998317`, 0.}, {1.3416407864998738`, 2.683281572999748}, { 1.7888543819998317`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, {1.3416407864998738`, 2.683281572999748}, { 1.7888543819998317`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 10}, {3, 4}, {3, 5}, {5, 6}, { 5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, {1.3416407864998738`, 2.683281572999748}, { 1.7888543819998317`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 4.47213595499958}, { 1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, {0.8944271909999159, 0.8944271909999162}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.3416407864998738`, 1.788854381999832}, {1.7888543819998317`, 2.683281572999748}, {2.23606797749979, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 10}, {3, 4}, {3, 9}, {4, 5}, { 4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 4.47213595499958}, { 1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, {0.8944271909999159, 0.8944271909999162}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.3416407864998738`, 1.788854381999832}, {1.7888543819998317`, 2.683281572999748}, {2.23606797749979, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, { 1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.683281572999748}, {2.6832815729997477`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 10}, {3, 4}, {3, 9}, {4, 5}, { 4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, {1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.683281572999748}, { 2.6832815729997477`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "Since at each step we have the choice of the left vertex or right vertex \ having children, there are ", Cell[BoxData[ FormBox[ SuperscriptBox["2", RowBox[{"n", "-", "2"}]], TraditionalForm]]], " ", Cell[BoxData[ FormBox["n", TraditionalForm]]], "-leaf path trees, and we can encode a path tree as a binary ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{"n", "-", "2"}], ")"}], TraditionalForm]]], "-tuple. ", StyleBox["PathTree", "Input"], " constructs a path tree from a list of zeros and ones." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "[", RowBox[{"PathTree", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1", ",", "0", ",", "1", ",", "1", ",", "0"}], "}"}], "]"}], "]"}]], "Input"], Cell[BoxData[ GraphicsBox[ TagBox[GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 7.155417527999327}, { 0.4472135954999579, 6.260990336999411}, {0., 5.366563145999495}, { 0.8944271909999159, 5.366563145999495}, {0.4472135954999579, 4.47213595499958}, {1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.5777087639996634`}, {0.4472135954999579, 2.6832815729997472`}, {1.3416407864998738`, 2.6832815729997472`}, { 0.8944271909999159, 1.7888543819998315`}, {1.7888543819998317`, 1.7888543819998315`}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {2.23606797749979, 0.8944271909999157}, {1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 6.260990336999411}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 17}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, {6, 16}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 15}, {12, 13}, { 12, 14}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 7.155417527999327}, { 0.4472135954999579, 6.260990336999411}, {0., 5.366563145999495}, { 0.8944271909999159, 5.366563145999495}, {0.4472135954999579, 4.47213595499958}, {1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.5777087639996634`}, {0.4472135954999579, 2.6832815729997472`}, {1.3416407864998738`, 2.6832815729997472`}, { 0.8944271909999159, 1.7888543819998315`}, {1.7888543819998317`, 1.7888543819998315`}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {2.23606797749979, 0.8944271909999157}, {1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 6.260990336999411}}]& ], AspectRatio->NCache[3^Rational[1, 2], 1.7320508075688772`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]]], "Output"] }, Open ]], Cell[TextData[{ StyleBox["FromPathTree", "Input"], " constructs the binary tuple encoding a path tree." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FromPathTree", "[", RowBox[{"First", "[", RowBox[{"PathTrees", "[", "10", "]"}], "]"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1", ",", "1"}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "The left comb tree is the path tree corresponding to ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{"0", ",", "0", ",", "\[Ellipsis]", ",", "0"}], "}"}], TraditionalForm]]], "; the right comb tree is the path tree corresponding to ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{"1", ",", "1", ",", "\[Ellipsis]", ",", "1"}], "}"}], TraditionalForm]]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"BareTreeForm", "[", RowBox[{"LeftCombTree", "[", "7", "]"}], "]"}], "\[IndentingNewLine]", RowBox[{"BareTreeForm", "[", RowBox[{"RightCombTree", "[", "7", "]"}], "]"}]}], "Input"], Cell[BoxData[ GraphicsBox[ TagBox[GraphicsGroupBox[{ GraphicsComplexBox[{{2.6832815729997477`, 5.366563145999495}, { 2.23606797749979, 4.47213595499958}, {1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.6832815729997477`}, { 2.6832815729997477`, 3.577708763999664}, {3.1304951684997055`, 4.47213595499958}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 13}, {2, 3}, {2, 12}, {3, 4}, {3, 11}, {4, 5}, {4, 10}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 4.47213595499958}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{2.6832815729997477`, 5.366563145999495}, { 2.23606797749979, 4.47213595499958}, {1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.6832815729997477`}, { 2.6832815729997477`, 3.577708763999664}, {3.1304951684997055`, 4.47213595499958}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]]], "Output"], Cell[BoxData[ GraphicsBox[ TagBox[GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.6832815729997477`}, { 1.7888543819998317`, 2.6832815729997477`}, {1.3416407864998738`, 1.788854381999832}, {2.23606797749979, 1.788854381999832}, { 1.7888543819998317`, 0.8944271909999157}, {2.6832815729997477`, 0.8944271909999157}, {2.23606797749979, 0.}, {3.1304951684997055`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 13}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.6832815729997477`}, { 1.7888543819998317`, 2.6832815729997477`}, {1.3416407864998738`, 1.788854381999832}, {2.23606797749979, 1.788854381999832}, { 1.7888543819998317`, 0.8944271909999157}, {2.6832815729997477`, 0.8944271909999157}, {2.23606797749979, 0.}, {3.1304951684997055`, 0.}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]]], "Output"] }, Open ]], Cell[TextData[{ StyleBox["LeftCrookedTree", "Input"], StyleBox[" and ", "Text", FontWeight->"Plain"], StyleBox["RightCrookedTree", "Input"], " give trees that alternate on each level." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"BareTreeForm", "[", RowBox[{"LeftCrookedTree", "[", "7", "]"}], "]"}], "\[IndentingNewLine]", RowBox[{"BareTreeForm", "[", RowBox[{"RightCrookedTree", "[", "7", "]"}], "]"}]}], "Input"], Cell[BoxData[ GraphicsBox[ TagBox[GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}, { 1.3416407864998738`, 4.47213595499958}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 13}, {2, 3}, {2, 4}, {4, 5}, {4, 12}, {5, 6}, {5, 7}, {7, 8}, {7, 11}, {8, 9}, {8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, { 1.3416407864998738`, 2.6832815729997477`}, {1.3416407864998738`, 4.47213595499958}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]]], "Output"], Cell[BoxData[ GraphicsBox[ TagBox[GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.6832815729997477`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, {1.3416407864998738`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 13}, {4, 5}, {4, 6}, {6, 7}, {6, 12}, {7, 8}, {7, 9}, {9, 10}, {9, 11}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.6832815729997477`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, {1.3416407864998738`, 3.577708763999664}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]]], "Output"] }, Open ]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Package symbols", "Section"], Cell[CellGroupData[{ Cell[TextData[StyleBox["BareTreeForm", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "BareTreeForm"}]], "Input"], Cell[BoxData[ StyleBox["\<\"BareTreeForm[expr] displays expr as an unlabeled tree with \ coloring to indicate instances of __ and ___.\"\>", "MSG"]], "Print", \ "PrintUsage", CellTags->"Info3502571694-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"BinaryTrees", "[", "5", "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8340576562282991, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, {2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, {2.502172968684897, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 7}, {4, 5}, {4, 6}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.502172968684897, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8340576562282991, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, {2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, {2.502172968684897, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, { 1.7888543819998317`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, {0.8340576562282991, 0.8340576562282993}, { 2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, {2.5021729686848975`, 0.8340576562282993}, { 2.0851441405707476`, 0.}, {2.919201796799047, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.919201796799047, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, { 2.5021729686848975`, 0.8340576562282993}, {2.0851441405707476`, 0.}, { 2.919201796799047, 0.}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, {0.8340576562282991, 0.8340576562282993}, { 2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, {1.2510864843424487`, 0.}, {2.0851441405707476`, 0.}, {2.5021729686848975`, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, { 1.2510864843424487`, 0.}, {2.0851441405707476`, 0.}, { 2.5021729686848975`, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, {0.8340576562282991, 0.8340576562282993}, { 0.41702882811414954`, 0.}, {1.2510864843424487`, 0.}, { 2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, {2.5021729686848975`, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {0.41702882811414954`, 0.}, { 1.2510864843424487`, 0.}, {2.0851441405707476`, 1.6681153124565984`}, { 1.6681153124565982`, 0.8340576562282993}, {2.5021729686848975`, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.6681153124565982`, 2.5021729686848975`}, { 0.8340576562282991, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 1.2510864843424487`, 0.8340576562282993}, {2.5021729686848975`, 1.6681153124565984`}, {2.0851441405707476`, 0.8340576562282993}, { 2.919201796799047, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 6}, {3, 4}, {3, 5}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.919201796799047, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.6681153124565982`, 2.5021729686848975`}, { 0.8340576562282991, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 1.2510864843424487`, 0.8340576562282993}, {2.5021729686848975`, 1.6681153124565984`}, {2.0851441405707476`, 0.8340576562282993}, { 2.919201796799047, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.6681153124565982`, 2.5021729686848975`}, { 1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, { 2.5021729686848975`, 0.}, {2.0851441405707476`, 1.6681153124565984`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 6}, {3, 4}, {3, 5}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.6681153124565982`, 2.5021729686848975`}, { 1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, { 2.5021729686848975`, 0.}, {2.0851441405707476`, 1.6681153124565984`}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 5}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 7}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "The option ", StyleBox["LevelHeight", "Input"], " can be used to adjust the size." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"BareTreeForm", "[", RowBox[{"#1", ",", RowBox[{"LevelHeight", "\[Rule]", "20"}]}], "]"}], "&"}], ")"}], "/@", RowBox[{"BinaryTrees", "[", "5", "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8340576562282991, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, {2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, {2.502172968684897, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 7}, {4, 5}, {4, 6}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.502172968684897, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8340576562282991, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, {2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, {2.502172968684897, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, { 1.7888543819998317`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, {0.8340576562282991, 0.8340576562282993}, { 2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, {2.5021729686848975`, 0.8340576562282993}, { 2.0851441405707476`, 0.}, {2.919201796799047, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.919201796799047, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, { 2.5021729686848975`, 0.8340576562282993}, {2.0851441405707476`, 0.}, { 2.919201796799047, 0.}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, {0.8340576562282991, 0.8340576562282993}, { 2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, {1.2510864843424487`, 0.}, {2.0851441405707476`, 0.}, {2.5021729686848975`, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, { 1.2510864843424487`, 0.}, {2.0851441405707476`, 0.}, { 2.5021729686848975`, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, {0.8340576562282991, 0.8340576562282993}, { 0.41702882811414954`, 0.}, {1.2510864843424487`, 0.}, { 2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, {2.5021729686848975`, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {0.41702882811414954`, 0.}, { 1.2510864843424487`, 0.}, {2.0851441405707476`, 1.6681153124565984`}, { 1.6681153124565982`, 0.8340576562282993}, {2.5021729686848975`, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.6681153124565982`, 2.5021729686848975`}, { 0.8340576562282991, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 1.2510864843424487`, 0.8340576562282993}, {2.5021729686848975`, 1.6681153124565984`}, {2.0851441405707476`, 0.8340576562282993}, { 2.919201796799047, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 6}, {3, 4}, {3, 5}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.919201796799047, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.6681153124565982`, 2.5021729686848975`}, { 0.8340576562282991, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 1.2510864843424487`, 0.8340576562282993}, {2.5021729686848975`, 1.6681153124565984`}, {2.0851441405707476`, 0.8340576562282993}, { 2.919201796799047, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.6681153124565982`, 2.5021729686848975`}, { 1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, { 2.5021729686848975`, 0.}, {2.0851441405707476`, 1.6681153124565984`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 6}, {3, 4}, {3, 5}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.6681153124565982`, 2.5021729686848975`}, { 1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, { 2.5021729686848975`, 0.}, {2.0851441405707476`, 1.6681153124565984`}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 5}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 7}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["BinaryTree", "Input"], StyleBox[" and ", FontWeight->"Plain"], StyleBox["FromBinaryTree", "Input"] }], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "BinaryTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"BinaryTree[tree] gives the binary tree corresponding to a \ tree.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571699-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BinaryTree", "[", RowBox[{ RowBox[{"Trees", "[", "5", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "FromBinaryTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"FromBinaryTree[binarytree] gives the tree corresponding to a \ binary tree.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571701-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FromBinaryTree", "[", RowBox[{ RowBox[{"BinaryTrees", "[", "5", "]"}], "\[LeftDoubleBracket]", "1", "\[RightDoubleBracket]"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["BinaryTreeQ", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "BinaryTreeQ"}]], "Input"], Cell[BoxData[ StyleBox["\<\"BinaryTreeQ[expr] gives True if expr is a binary tree, and \ False otherwise.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571704-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BinaryTreeQ", "/@", RowBox[{"Trees", "[", "5", "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ "False", ",", "False", ",", "False", ",", "False", ",", "False", ",", "False", ",", "True", ",", "False", ",", "False", ",", "True", ",", "False", ",", "False", ",", "False", ",", "False"}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["BinaryTrees", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "BinaryTrees"}]], "Input"], Cell[BoxData[ StyleBox["\<\"BinaryTrees[n] gives a list of all binary trees with n leaves.\ \"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571705-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"BinaryTrees", "[", "5", "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8340576562282991, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, {2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, {2.502172968684897, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 7}, {4, 5}, {4, 6}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.502172968684897, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8340576562282991, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, {2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, {2.502172968684897, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, { 1.7888543819998317`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, {0.8340576562282991, 0.8340576562282993}, { 2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, {2.5021729686848975`, 0.8340576562282993}, { 2.0851441405707476`, 0.}, {2.919201796799047, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.919201796799047, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, { 2.5021729686848975`, 0.8340576562282993}, {2.0851441405707476`, 0.}, { 2.919201796799047, 0.}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, {0.8340576562282991, 0.8340576562282993}, { 2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, {1.2510864843424487`, 0.}, {2.0851441405707476`, 0.}, {2.5021729686848975`, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, { 1.2510864843424487`, 0.}, {2.0851441405707476`, 0.}, { 2.5021729686848975`, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, {0.8340576562282991, 0.8340576562282993}, { 0.41702882811414954`, 0.}, {1.2510864843424487`, 0.}, { 2.0851441405707476`, 1.6681153124565984`}, {1.6681153124565982`, 0.8340576562282993}, {2.5021729686848975`, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2510864843424487`, 2.5021729686848975`}, { 0.41702882811414954`, 1.6681153124565984`}, {0., 0.8340576562282993}, { 0.8340576562282991, 0.8340576562282993}, {0.41702882811414954`, 0.}, { 1.2510864843424487`, 0.}, {2.0851441405707476`, 1.6681153124565984`}, { 1.6681153124565982`, 0.8340576562282993}, {2.5021729686848975`, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.6681153124565982`, 2.5021729686848975`}, { 0.8340576562282991, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 1.2510864843424487`, 0.8340576562282993}, {2.5021729686848975`, 1.6681153124565984`}, {2.0851441405707476`, 0.8340576562282993}, { 2.919201796799047, 0.8340576562282993}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 6}, {3, 4}, {3, 5}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{2.919201796799047, 0.8340576562282993}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.6681153124565982`, 2.5021729686848975`}, { 0.8340576562282991, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 1.2510864843424487`, 0.8340576562282993}, {2.5021729686848975`, 1.6681153124565984`}, {2.0851441405707476`, 0.8340576562282993}, { 2.919201796799047, 0.8340576562282993}}]& ], AspectRatio->NCache[2 5^Rational[-1, 2], 0.8944271909999159], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.6681153124565982`, 2.5021729686848975`}, { 1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, { 2.5021729686848975`, 0.}, {2.0851441405707476`, 1.6681153124565984`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 6}, {3, 4}, {3, 5}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 1.6681153124565984`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 0.8340576562282993}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 1.6681153124565984`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.6681153124565982`, 2.5021729686848975`}, { 1.2510864843424487`, 1.6681153124565984`}, {0.41702882811414954`, 0.8340576562282993}, {0., 0.}, {0.8340576562282991, 0.}, { 2.0851441405707476`, 0.8340576562282993}, {1.6681153124565982`, 0.}, { 2.5021729686848975`, 0.}, {2.0851441405707476`, 1.6681153124565984`}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 5}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 7}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["CompleteBinaryTree", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "CompleteBinaryTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"CompleteBinaryTree[2^n] gives the binary tree with 2^n leaves, \ all on the lowest level.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571707-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"BareTreeForm", "[", RowBox[{"CompleteBinaryTree", "[", SuperscriptBox["2", "n"], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "4"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[{{0., 0.}}, {RGBColor[0.55, 0.45, 0.45]}], {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0., 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.2247448713915892`, 1.6329931618554523`}, { 0.4082482904638631, 0.8164965809277261}, {0., 0.}, { 0.8164965809277261, 0.}, {2.041241452319315, 0.8164965809277261}, { 1.6329931618554523`, 0.}, {2.4494897427831783`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.2247448713915892`, 1.6329931618554523`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4082482904638631, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.041241452319315, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6329931618554523`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.4494897427831783`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.2247448713915892`, 1.6329931618554523`}, { 0.4082482904638631, 0.8164965809277261}, {0., 0.}, {0.8164965809277261, 0.}, {2.041241452319315, 0.8164965809277261}, {1.6329931618554523`, 0.}, {2.4494897427831783`, 0.}}]& ], AspectRatio->NCache[Rational[1, 2] 3^Rational[1, 2], 0.8660254037844386], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{2.4748737341529163`, 2.1213203435596424`}, { 1.0606601717798212`, 1.414213562373095}, {0.35355339059327373`, 0.7071067811865475}, {0., 0.}, {0.7071067811865475, 0.}, { 1.7677669529663687`, 0.7071067811865475}, {1.414213562373095, 0.}, { 2.1213203435596424`, 0.}, {3.8890872965260113`, 1.414213562373095}, { 3.181980515339464, 0.7071067811865475}, {2.82842712474619, 0.}, { 3.5355339059327373`, 0.}, {4.596194077712559, 0.7071067811865475}, { 4.242640687119285, 0.}, {4.949747468305833, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 6}, {3, 4}, {3, 5}, {6, 7}, {6, 8}, {9, 10}, {9, 13}, {10, 11}, {10, 12}, {13, 14}, {13, 15}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.4748737341529163`, 2.1213203435596424`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.0606601717798212`, 1.414213562373095}]}, {RGBColor[0, 0, 0.7], PointBox[{0.35355339059327373`, 0.7071067811865475}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7071067811865475, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7677669529663687`, 0.7071067811865475}]}, {RGBColor[0, 0, 0.7], PointBox[{1.414213562373095, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.1213203435596424`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.8890872965260113`, 1.414213562373095}]}, {RGBColor[0, 0, 0.7], PointBox[{3.181980515339464, 0.7071067811865475}]}, {RGBColor[0, 0, 0.7], PointBox[{2.82842712474619, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5355339059327373`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.596194077712559, 0.7071067811865475}]}, {RGBColor[0, 0, 0.7], PointBox[{4.242640687119285, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.949747468305833, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{2.4748737341529163`, 2.1213203435596424`}, { 1.0606601717798212`, 1.414213562373095}, {0.35355339059327373`, 0.7071067811865475}, {0., 0.}, {0.7071067811865475, 0.}, { 1.7677669529663687`, 0.7071067811865475}, {1.414213562373095, 0.}, { 2.1213203435596424`, 0.}, {3.8890872965260113`, 1.414213562373095}, { 3.181980515339464, 0.7071067811865475}, {2.82842712474619, 0.}, { 3.5355339059327373`, 0.}, {4.596194077712559, 0.7071067811865475}, { 4.242640687119285, 0.}, {4.949747468305833, 0.}}]& ], AspectRatio->NCache[2^Rational[-1, 2], 0.7071067811865475], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGCQB2IQ/Vrf/CJPkKCDrPEE1+WVTA47de7FFGkxOKzxiXhR te23/Wow/doeIv8JSl+ylwPTj+wZ0IAsmvgT+y9ighLf4eph5sDkV0PtgfHd 3Zb9d03ndICpa7B00rtzgsUBVT+TA6r57HA+XzDXxfWsfHD1EPO54fIQ/wnA +ZWe/4sf9EnB/bvJZvaisg+icPv9zF7udFwojGa/EFw/xH0icL6Ys2/3ansJ uHqI+8Th8hD/ScL5DmHJrl668nD77vpvjBG9J4Pmfmk0/8nB+UHruKbb71OA q4f4TwEuD4lfRTgfALxPla0= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 17}, {2, 3}, {2, 10}, {3, 4}, {3, 7}, {4, 5}, { 4, 6}, {7, 8}, {7, 9}, {10, 11}, {10, 14}, {11, 12}, {11, 13}, {14, 15}, {14, 16}, {17, 18}, {17, 25}, {18, 19}, {18, 22}, {19, 20}, { 19, 21}, {22, 23}, {22, 24}, {25, 26}, {25, 29}, {26, 27}, {26, 28}, {29, 30}, {29, 31}}]}], { {RGBColor[0, 0, 0.7], PointBox[{4.330127018922194, 2.3094010767585034`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0207259421636903`, 1.7320508075688776`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8660254037844387, 1.1547005383792517`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.2886751345948129, 0.577350269189626}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.5773502691896258, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.4433756729740645`, 0.577350269189626}]}, {RGBColor[0, 0, 0.7], PointBox[{1.1547005383792517`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7320508075688774`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1754264805429417`, 1.1547005383792517`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.598076211353316, 0.577350269189626}]}, {RGBColor[0, 0, 0.7], PointBox[{2.3094010767585034`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.886751345948129, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.7527767497325675`, 0.577350269189626}]}, {RGBColor[0, 0, 0.7], PointBox[{3.464101615137755, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.041451884327381, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{6.639528095680697, 1.7320508075688776`}]}, {RGBColor[0, 0, 0.7], PointBox[{5.484827557301445, 1.1547005383792517`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.907477288111819, 0.577350269189626}]}, {RGBColor[0, 0, 0.7], PointBox[{4.618802153517007, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{5.196152422706632, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{6.062177826491071, 0.577350269189626}]}, {RGBColor[0, 0, 0.7], PointBox[{5.773502691896258, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{6.3508529610858835`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{7.794228634059948, 1.1547005383792517`}]}, {RGBColor[0, 0, 0.7], PointBox[{7.216878364870323, 0.577350269189626}]}, {RGBColor[0, 0, 0.7], PointBox[{6.92820323027551, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{7.505553499465135, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{8.371578903249574, 0.577350269189626}]}, {RGBColor[0, 0, 0.7], PointBox[{8.082903768654761, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{8.660254037844387, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGCQB2IQ/Vrf/CJPkKCDrPEE1+WVTA47de7FFGkxOKzxiXhR te23/Wow/doeIv8JSl+ylwPTj+wZ0IAsmvgT+y9ighLf4eph5sDkV0PtgfHd 3Zb9d03ndICpa7B00rtzgsUBVT+TA6r57HA+XzDXxfWsfHD1EPO54fIQ/wnA +ZWe/4sf9EnB/bvJZvaisg+icPv9zF7udFwojGa/EFw/xH0icL6Ys2/3ansJ uHqI+8Th8hD/ScL5DmHJrl668nD77vpvjBG9J4Pmfmk0/8nB+UHruKbb71OA q4f4TwEuD4lfRTgfALxPla0= "]]& ], AspectRatio->NCache[Rational[1, 4] 5^Rational[1, 2], 0.5590169943749475], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["DyckWord", "Input"], StyleBox[" and ", FontWeight->"Plain"], StyleBox["FromDyckWord", "Input"] }], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "DyckWord"}]], "Input"], Cell[BoxData[ StyleBox["\<\"DyckWord[tree] gives the Dyck word corresponding to a \ tree.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571710-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DyckWord", "/@", RowBox[{"Trees", "[", "5", "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"\<\"00001111\"\>", ",", "\<\"00010111\"\>", ",", "\<\"00100111\"\>", ",", "\<\"00011011\"\>", ",", "\<\"00101011\"\>", ",", "\<\"01000111\"\>", ",", "\<\"01001011\"\>", ",", "\<\"00110011\"\>", ",", "\<\"00011101\"\>", ",", "\<\"00101101\"\>", ",", "\<\"01010011\"\>", ",", "\<\"01001101\"\>", ",", "\<\"00110101\"\>", ",", "\<\"01010101\"\>"}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "FromDyckWord"}]], "Input"], Cell[BoxData[ StyleBox["\<\"FromDyckWord[word] gives the tree corresponding to a Dyck \ word.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571712-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"FromDyckWord", "/@", RowBox[{"DyckWords", "[", "4", "]"}]}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1., 0.6666666666666666}, {0., 0.}, { 0.6666666666666666, 0.}, {1.3333333333333333`, 0.}, {2., 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {1, 4}, {1, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1., 0.6666666666666666}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.6666666666666666, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3333333333333333`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2., 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1., 0.6666666666666666}, {0., 0.}, { 0.6666666666666666, 0.}, {1.3333333333333333`, 0.}, {2., 0.}}]& ], AspectRatio->NCache[2^Rational[-1, 2], 0.7071067811865475], FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8164965809277261, 1.6329931618554523`}, {0., 0.8164965809277261}, {0.8164965809277261, 0.8164965809277261}, { 1.6329931618554523`, 0.8164965809277261}, {1.6329931618554523`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {1, 4}, {4, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 1.6329931618554523`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6329931618554523`, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6329931618554523`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8164965809277261, 1.6329931618554523`}, { 0., 0.8164965809277261}, {0.8164965809277261, 0.8164965809277261}, { 1.6329931618554523`, 0.8164965809277261}, {1.6329931618554523`, 0.}}]& ], AspectRatio->NCache[Rational[1, 2] 3^Rational[1, 2], 0.8660254037844386], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999159}, {0.8944271909999159, 0.8944271909999159}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 1.7888543819998317`}, { 0., 0.8944271909999159}, {0.8944271909999159, 0.8944271909999159}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.47140452079103173`, 2.8284271247461903`}, {0., 1.8856180831641267`}, {0.9428090415820635, 1.8856180831641267`}, { 0.9428090415820635, 0.9428090415820634}, {0.9428090415820635, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {4, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 2.8284271247461903`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.8856180831641267`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 1.8856180831641267`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 0.9428090415820634}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.47140452079103173`, 2.8284271247461903`}, { 0., 1.8856180831641267`}, {0.9428090415820635, 1.8856180831641267`}, { 0.9428090415820635, 0.9428090415820634}, {0.9428090415820635, 0.}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8164965809277261, 1.6329931618554523`}, {0., 0.8164965809277261}, {0.8164965809277261, 0.8164965809277261}, { 0.8164965809277261, 0.}, {1.6329931618554523`, 0.8164965809277261}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {1, 5}, {3, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 1.6329931618554523`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6329931618554523`, 0.8164965809277261}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8164965809277261, 1.6329931618554523`}, { 0., 0.8164965809277261}, {0.8164965809277261, 0.8164965809277261}, { 0.8164965809277261, 0.}, {1.6329931618554523`, 0.8164965809277261}}]& ], AspectRatio->NCache[Rational[1, 2] 3^Rational[1, 2], 0.8660254037844386], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8164965809277261, 1.6329931618554523`}, { 0.8164965809277261, 0.8164965809277261}, {0., 0.}, { 0.8164965809277261, 0.}, {1.6329931618554523`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {2, 4}, {2, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 1.6329931618554523`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6329931618554523`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8164965809277261, 1.6329931618554523`}, { 0.8164965809277261, 0.8164965809277261}, {0., 0.}, {0.8164965809277261, 0.}, {1.6329931618554523`, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.47140452079103173`, 2.8284271247461903`}, { 0.47140452079103173`, 1.8856180831641267`}, {0., 0.9428090415820634}, {0.9428090415820635, 0.9428090415820634}, { 0.9428090415820635, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {2, 4}, {4, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 2.8284271247461903`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 1.8856180831641267`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9428090415820634}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 0.9428090415820634}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.47140452079103173`, 2.8284271247461903`}, { 0.47140452079103173`, 1.8856180831641267`}, {0., 0.9428090415820634}, { 0.9428090415820635, 0.9428090415820634}, {0.9428090415820635, 0.}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.47140452079103173`, 2.8284271247461903`}, { 0.47140452079103173`, 1.8856180831641267`}, {0.47140452079103173`, 0.9428090415820634}, {0., 0.}, {0.9428090415820635, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {3, 4}, {3, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 2.8284271247461903`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 1.8856180831641267`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 0.9428090415820634}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.47140452079103173`, 2.8284271247461903`}, { 0.47140452079103173`, 1.8856180831641267`}, {0.47140452079103173`, 0.9428090415820634}, {0., 0.}, {0.9428090415820635, 0.}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0., 4.}, {0., 3.}, {0., 2.}, {0., 1.}, {0., 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {3, 4}, {4, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0., 4.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0., 4.}, {0., 3.}, {0., 2.}, {0., 1.}, {0., 0.}}]& ], AspectRatio->NCache[Rational[5, 2]^Rational[1, 2], 1.5811388300841898`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.47140452079103173`, 2.8284271247461903`}, { 0.47140452079103173`, 1.8856180831641267`}, {0., 0.9428090415820634}, {0., 0.}, {0.9428090415820635, 0.9428090415820634}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {2, 3}, {2, 5}, {3, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 2.8284271247461903`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 1.8856180831641267`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9428090415820634}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 0.9428090415820634}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.47140452079103173`, 2.8284271247461903`}, { 0.47140452079103173`, 1.8856180831641267`}, {0., 0.9428090415820634}, { 0., 0.}, {0.9428090415820635, 0.9428090415820634}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8164965809277261, 1.6329931618554523`}, {0., 0.8164965809277261}, {0., 0.}, {0.8164965809277261, 0.8164965809277261}, {1.6329931618554523`, 0.8164965809277261}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 4}, {1, 5}, {2, 3}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 1.6329931618554523`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8164965809277261, 0.8164965809277261}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6329931618554523`, 0.8164965809277261}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8164965809277261, 1.6329931618554523`}, { 0., 0.8164965809277261}, {0., 0.}, {0.8164965809277261, 0.8164965809277261}, {1.6329931618554523`, 0.8164965809277261}}]& ], AspectRatio->NCache[Rational[1, 2] 3^Rational[1, 2], 0.8660254037844386], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.47140452079103173`, 1.885618083164127}, {0., 0.9428090415820635}, {0., 0.}, {0.9428090415820635, 0.9428090415820635}, {0.9428090415820635, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 4}, {2, 3}, {4, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 1.885618083164127}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9428090415820635}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 0.9428090415820635}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.47140452079103173`, 1.885618083164127}, { 0., 0.9428090415820635}, {0., 0.}, {0.9428090415820635, 0.9428090415820635}, {0.9428090415820635, 0.}}]& ], AspectRatio->NCache[Rational[1, 2] 3^Rational[1, 2], 0.8660254037844386], FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999159}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999159}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999159}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999159}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.47140452079103173`, 2.8284271247461903`}, {0., 1.8856180831641267`}, {0., 0.9428090415820634}, {0., 0.}, { 0.9428090415820635, 1.8856180831641267`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {3, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.47140452079103173`, 2.8284271247461903`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.8856180831641267`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.9428090415820634}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9428090415820635, 1.8856180831641267`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.47140452079103173`, 2.8284271247461903`}, { 0., 1.8856180831641267`}, {0., 0.9428090415820634}, {0., 0.}, { 0.9428090415820635, 1.8856180831641267`}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["DyckWordQ", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "DyckWordQ"}]], "Input"], Cell[BoxData[ StyleBox["\<\"DyckWordQ[string] gives True if string is a Dyck word on \ {\\\"0\\\", \\\"1\\\"}, and False otherwise.\"\>", "MSG"]], "Print", \ "PrintUsage", CellTags->"Info3502571715-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DyckWordQ", "[", "\"\<0110\>\"", "]"}]], "Input"], Cell[BoxData["False"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DyckWordQ", "[", "\"\<0101\>\"", "]"}]], "Input"], Cell[BoxData["True"], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["DyckWords", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "DyckWords"}]], "Input"], Cell[BoxData[ StyleBox["\<\"DyckWords[n] gives a list of the length\[Hyphen]2n Dyck words \ on {\\\"0\\\", \\\"1\\\"}.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571717-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"DyckWords", "[", "4", "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{"\<\"01010101\"\>", ",", "\<\"01010011\"\>", ",", "\<\"01001011\"\>", ",", "\<\"01000111\"\>", ",", "\<\"01001101\"\>", ",", "\<\"00101011\"\>", ",", "\<\"00100111\"\>", ",", "\<\"00010111\"\>", ",", "\<\"00001111\"\>", ",", "\<\"00011011\"\>", ",", "\<\"00110101\"\>", ",", "\<\"00110011\"\>", ",", "\<\"00101101\"\>", ",", "\<\"00011101\"\>"}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["LeftCombTree", "Input"], StyleBox[" and ", "Text", FontWeight->"Plain"], StyleBox["RightCombTree", "Input"] }], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "LeftCombTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"LeftCombTree[n] gives the n\[Hyphen]leaf path tree in which \ only the left child of a vertex has children.\"\>", "MSG"]], "Print", \ "PrintUsage", CellTags->"Info3502571721-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"LeftCombTree", "/@", RowBox[{"Range", "[", "10", "]"}]}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[{{0., 0.}}, {RGBColor[0.55, 0.45, 0.45]}], {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0., 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999159}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999159}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999159}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999159}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.894427190999916}, {1.7888543819998317`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 6}, {3, 4}, {3, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.894427190999916}, {1.7888543819998317`, 1.788854381999832}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 7}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, { 1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.683281572999748}, {2.6832815729997477`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 10}, {3, 4}, {3, 9}, {4, 5}, { 4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, {1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.683281572999748}, { 2.6832815729997477`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{2.6832815729997477`, 5.366563145999495}, { 2.23606797749979, 4.47213595499958}, {1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.6832815729997477`}, { 2.6832815729997477`, 3.577708763999664}, {3.1304951684997055`, 4.47213595499958}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 13}, {2, 3}, {2, 12}, {3, 4}, {3, 11}, {4, 5}, { 4, 10}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 4.47213595499958}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{2.6832815729997477`, 5.366563145999495}, { 2.23606797749979, 4.47213595499958}, {1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.6832815729997477`}, { 2.6832815729997477`, 3.577708763999664}, {3.1304951684997055`, 4.47213595499958}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{3.1304951684997055`, 6.260990336999411}, { 2.6832815729997477`, 5.366563145999495}, {2.23606797749979, 4.47213595499958}, {1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998315`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998315`}, { 2.23606797749979, 2.6832815729997477`}, {2.6832815729997477`, 3.5777087639996634`}, {3.1304951684997055`, 4.47213595499958}, { 3.5777087639996634`, 5.366563145999495}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 15}, {2, 3}, {2, 14}, {3, 4}, {3, 13}, {4, 5}, { 4, 12}, {5, 6}, {5, 11}, {6, 7}, {6, 10}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 5.366563145999495}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{3.1304951684997055`, 6.260990336999411}, { 2.6832815729997477`, 5.366563145999495}, {2.23606797749979, 4.47213595499958}, {1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998315`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998315`}, { 2.23606797749979, 2.6832815729997477`}, {2.6832815729997477`, 3.5777087639996634`}, {3.1304951684997055`, 4.47213595499958}, { 3.5777087639996634`, 5.366563145999495}}]& ], AspectRatio->NCache[2 Rational[2, 3]^Rational[1, 2], 1.632993161855452], FrameTicks->Automatic, ImageSize->{Automatic, 70}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{3.5777087639996634`, 7.155417527999327}, { 3.1304951684997055`, 6.260990336999411}, {2.6832815729997477`, 5.366563145999495}, {2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.5777087639996634`}, {1.3416407864998738`, 2.6832815729997472`}, {0.8944271909999159, 1.7888543819998315`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, { 1.7888543819998317`, 1.7888543819998315`}, {2.23606797749979, 2.6832815729997472`}, {2.6832815729997477`, 3.5777087639996634`}, { 3.1304951684997055`, 4.47213595499958}, {3.5777087639996634`, 5.366563145999495}, {4.024922359499621, 6.260990336999411}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 17}, {2, 3}, {2, 16}, {3, 4}, {3, 15}, {4, 5}, { 4, 14}, {5, 6}, {5, 13}, {6, 7}, {6, 12}, {7, 8}, {7, 11}, {8, 9}, { 8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 6.260990336999411}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{3.5777087639996634`, 7.155417527999327}, { 3.1304951684997055`, 6.260990336999411}, {2.6832815729997477`, 5.366563145999495}, {2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.5777087639996634`}, {1.3416407864998738`, 2.6832815729997472`}, {0.8944271909999159, 1.7888543819998315`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998315`}, {2.23606797749979, 2.6832815729997472`}, { 2.6832815729997477`, 3.5777087639996634`}, {3.1304951684997055`, 4.47213595499958}, {3.5777087639996634`, 5.366563145999495}, { 4.024922359499621, 6.260990336999411}}]& ], AspectRatio->NCache[3^Rational[1, 2], 1.7320508075688772`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBmIQfeqrtX2rpIADhFZwuPl2/1HV+TxQWsZB7gM7ryM3 J5SWdEj+5B8SU87qkASmRR1WfJk+u/wxI5QWhOr7Y38Dag5E/Vf7JKg+iPwb qPwfewj/DpT/xp4BDdxEE4eZB1OPat8fe5h7YPbB3AtzD8w/qO7lgfsHFh4w /6Kqk3EAANhbjGA= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 19}, {2, 3}, {2, 18}, {3, 4}, {3, 17}, {4, 5}, { 4, 16}, {5, 6}, {5, 15}, {6, 7}, {6, 14}, {7, 8}, {7, 13}, {8, 9}, { 8, 12}, {9, 10}, {9, 11}}]}], { {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{4.47213595499958, 7.155417527999327}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGAQBmIQfeqrtX2rpIADhFZwuPl2/1HV+TxQWsZB7gM7ryM3 J5SWdEj+5B8SU87qkASmRR1WfJk+u/wxI5QWhOr7Y38Dag5E/Vf7JKg+iPwb qPwfewj/DpT/xp4BDdxEE4eZB1OPat8fe5h7YPbB3AtzD8w/qO7lgfsHFh4w /6Kqk3EAANhbjGA= "]]& ], AspectRatio->NCache[Rational[10, 3]^Rational[1, 2], 1.8257418583505538`], FrameTicks->Automatic, ImageSize->{Automatic, 90}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "RightCombTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"RightCombTree[n] gives the n\[Hyphen]leaf path tree in which \ only the right child of a vertex has children.\"\>", "MSG"]], "Print", \ "PrintUsage", CellTags->"Info3502571724-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"RightCombTree", "/@", RowBox[{"Range", "[", "10", "]"}]}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[{{0., 0.}}, {RGBColor[0.55, 0.45, 0.45]}], {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0., 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999159}, {0.8944271909999159, 0.8944271909999159}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 1.7888543819998317`}, { 0., 0.8944271909999159}, {0.8944271909999159, 0.8944271909999159}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {1.3416407864998738`, 0.894427190999916}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 2.6832815729997477`}, { 0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {1.3416407864998738`, 0.894427190999916}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 1.7888543819998317`, 1.788854381999832}, {1.3416407864998738`, 0.8944271909999162}, {2.23606797749979, 0.8944271909999162}, { 1.7888543819998317`, 0.}, {2.6832815729997477`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 1.7888543819998317`, 1.788854381999832}, {1.3416407864998738`, 0.8944271909999162}, {2.23606797749979, 0.8944271909999162}, { 1.7888543819998317`, 0.}, {2.6832815729997477`, 0.}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.6832815729997477`}, { 1.7888543819998317`, 2.6832815729997477`}, {1.3416407864998738`, 1.788854381999832}, {2.23606797749979, 1.788854381999832}, { 1.7888543819998317`, 0.8944271909999157}, {2.6832815729997477`, 0.8944271909999157}, {2.23606797749979, 0.}, {3.1304951684997055`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 13}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.6832815729997477`}, { 1.7888543819998317`, 2.6832815729997477`}, {1.3416407864998738`, 1.788854381999832}, {2.23606797749979, 1.788854381999832}, { 1.7888543819998317`, 0.8944271909999157}, {2.6832815729997477`, 0.8944271909999157}, {2.23606797749979, 0.}, {3.1304951684997055`, 0.}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 6.260990336999411}, {0., 5.366563145999495}, {0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {1.3416407864998738`, 4.47213595499958}, {0.8944271909999159, 3.5777087639996634`}, { 1.7888543819998317`, 3.5777087639996634`}, {1.3416407864998738`, 2.6832815729997477`}, {2.23606797749979, 2.6832815729997477`}, { 1.7888543819998317`, 1.7888543819998315`}, {2.6832815729997477`, 1.7888543819998315`}, {2.23606797749979, 0.8944271909999157}, { 3.1304951684997055`, 0.8944271909999157}, {2.6832815729997477`, 0.}, { 3.5777087639996634`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 13}, {13, 14}, {13, 15}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 6.260990336999411}, {0., 5.366563145999495}, {0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {1.3416407864998738`, 4.47213595499958}, {0.8944271909999159, 3.5777087639996634`}, { 1.7888543819998317`, 3.5777087639996634`}, {1.3416407864998738`, 2.6832815729997477`}, {2.23606797749979, 2.6832815729997477`}, { 1.7888543819998317`, 1.7888543819998315`}, {2.6832815729997477`, 1.7888543819998315`}, {2.23606797749979, 0.8944271909999157}, { 3.1304951684997055`, 0.8944271909999157}, {2.6832815729997477`, 0.}, { 3.5777087639996634`, 0.}}]& ], AspectRatio->NCache[2 Rational[2, 3]^Rational[1, 2], 1.632993161855452], FrameTicks->Automatic, ImageSize->{Automatic, 70}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 7.155417527999327}, {0., 6.260990336999411}, {0.8944271909999159, 6.260990336999411}, { 0.4472135954999579, 5.366563145999495}, {1.3416407864998738`, 5.366563145999495}, {0.8944271909999159, 4.47213595499958}, { 1.7888543819998317`, 4.47213595499958}, {1.3416407864998738`, 3.5777087639996634`}, {2.23606797749979, 3.5777087639996634`}, { 1.7888543819998317`, 2.6832815729997472`}, {2.6832815729997477`, 2.6832815729997472`}, {2.23606797749979, 1.7888543819998315`}, { 3.1304951684997055`, 1.7888543819998315`}, {2.6832815729997477`, 0.8944271909999157}, {3.5777087639996634`, 0.8944271909999157}, { 3.1304951684997055`, 0.}, {4.024922359499621, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 13}, {13, 14}, {13, 15}, {15, 16}, {15, 17}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 7.155417527999327}, {0., 6.260990336999411}, {0.8944271909999159, 6.260990336999411}, { 0.4472135954999579, 5.366563145999495}, {1.3416407864998738`, 5.366563145999495}, {0.8944271909999159, 4.47213595499958}, { 1.7888543819998317`, 4.47213595499958}, {1.3416407864998738`, 3.5777087639996634`}, {2.23606797749979, 3.5777087639996634`}, { 1.7888543819998317`, 2.6832815729997472`}, {2.6832815729997477`, 2.6832815729997472`}, {2.23606797749979, 1.7888543819998315`}, { 3.1304951684997055`, 1.7888543819998315`}, {2.6832815729997477`, 0.8944271909999157}, {3.5777087639996634`, 0.8944271909999157}, { 3.1304951684997055`, 0.}, {4.024922359499621, 0.}}]& ], AspectRatio->NCache[3^Rational[1, 2], 1.7320508075688772`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBmIQffPt/qOq8+/Yn/pqbd8qqeDAAAUQcRkHCP3GHpV/ x17uAzuvI7ekQ/In/5CY8q9wPkx9ElhcFMr/A+fD1K/4Mn12+WNBBwjN6ADj w9TfANM8UPWsDjA+TH0SVBxiLyecj6r+D9TdPHA+TP0NqDsh/haA82HqYeEA cxeMDwD1Jo5i "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 13}, {13, 14}, {13, 15}, {15, 16}, {15, 17}, {17, 18}, {17, 19}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.47213595499958, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGAQBmIQffPt/qOq8+/Yn/pqbd8qqeDAAAUQcRkHCP3GHpV/ x17uAzuvI7ekQ/In/5CY8q9wPkx9ElhcFMr/A+fD1K/4Mn12+WNBBwjN6ADj w9TfANM8UPWsDjA+TH0SVBxiLyecj6r+D9TdPHA+TP0NqDsh/haA82HqYeEA cxeMDwD1Jo5i "]]& ], AspectRatio->NCache[Rational[10, 3]^Rational[1, 2], 1.8257418583505538`], FrameTicks->Automatic, ImageSize->{Automatic, 90}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["LeftCrookedTree", "Input"], StyleBox[" and ", "Text", FontWeight->"Plain"], StyleBox["RightCrookedTree", "Input"] }], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "LeftCrookedTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"LeftCrookedTree[n] gives the n\[Hyphen]leaf path tree in which \ alternate vertices on successive levels have children, beginning with the \ left child.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571726-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"LeftCrookedTree", "/@", RowBox[{"Range", "[", RowBox[{"2", ",", "10"}], "]"}]}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999159}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999159}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999159}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999159}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.894427190999916}, { 0.8944271909999159, 0.894427190999916}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 4}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.894427190999916}, { 0.8944271909999159, 0.894427190999916}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, {0.8944271909999159, 0.8944271909999162}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, {1.3416407864998738`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 4}, {4, 5}, {4, 10}, {5, 6}, { 5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, {0.8944271909999159, 0.8944271909999162}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, {1.3416407864998738`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}, { 1.3416407864998738`, 4.47213595499958}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 13}, {2, 3}, {2, 4}, {4, 5}, {4, 12}, {5, 6}, { 5, 7}, {7, 8}, {7, 11}, {8, 9}, {8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}, { 1.3416407864998738`, 4.47213595499958}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 6.260990336999411}, { 0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, { 0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998315`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.3416407864998738`, 1.7888543819998315`}, {1.3416407864998738`, 3.5777087639996634`}, {1.3416407864998738`, 5.366563145999495}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 15}, {2, 3}, {2, 4}, {4, 5}, {4, 14}, {5, 6}, { 5, 7}, {7, 8}, {7, 13}, {8, 9}, {8, 10}, {10, 11}, {10, 12}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999495}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 6.260990336999411}, { 0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, { 0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998315`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.3416407864998738`, 1.7888543819998315`}, {1.3416407864998738`, 3.5777087639996634`}, {1.3416407864998738`, 5.366563145999495}}]& ], AspectRatio->NCache[2 Rational[2, 3]^Rational[1, 2], 1.632993161855452], FrameTicks->Automatic, ImageSize->{Automatic, 70}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 7.155417527999327}, { 0.4472135954999579, 6.260990336999411}, {0., 5.366563145999495}, { 0.8944271909999159, 5.366563145999495}, {0.4472135954999579, 4.47213595499958}, {0., 3.5777087639996634`}, {0.8944271909999159, 3.5777087639996634`}, {0.4472135954999579, 2.6832815729997472`}, {0., 1.7888543819998315`}, {0.8944271909999159, 1.7888543819998315`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, { 1.3416407864998738`, 2.6832815729997472`}, {1.3416407864998738`, 4.47213595499958}, {1.3416407864998738`, 6.260990336999411}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 17}, {2, 3}, {2, 4}, {4, 5}, {4, 16}, {5, 6}, { 5, 7}, {7, 8}, {7, 15}, {8, 9}, {8, 10}, {10, 11}, {10, 14}, {11, 12}, {11, 13}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 7.155417527999327}, { 0.4472135954999579, 6.260990336999411}, {0., 5.366563145999495}, { 0.8944271909999159, 5.366563145999495}, {0.4472135954999579, 4.47213595499958}, {0., 3.5777087639996634`}, {0.8944271909999159, 3.5777087639996634`}, {0.4472135954999579, 2.6832815729997472`}, {0., 1.7888543819998315`}, {0.8944271909999159, 1.7888543819998315`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997472`}, {1.3416407864998738`, 4.47213595499958}, { 1.3416407864998738`, 6.260990336999411}}]& ], AspectRatio->NCache[3^Rational[1, 2], 1.7320508075688772`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBmIQffPt/qOq89/Yn/pqbd8qqeAA4d+xh9AyDgxQIPeB ndeRW9IBph6Vf8c+6ZN/SEy5KFz9ii/TZ5c/FoSrR+Xfsb8Bpnng6iH6WeHq Ufkw9X/sYepvQNXB1KPy78DVJYPN+YrBh5mHyudxgPFh/oHxYeEBALdOjD8= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 19}, {2, 3}, {2, 4}, {4, 5}, {4, 18}, {5, 6}, { 5, 7}, {7, 8}, {7, 17}, {8, 9}, {8, 10}, {10, 11}, {10, 16}, {11, 12}, {11, 13}, {13, 14}, {13, 15}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 7.155417527999327}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGAQBmIQffPt/qOq89/Yn/pqbd8qqeAA4d+xh9AyDgxQIPeB ndeRW9IBph6Vf8c+6ZN/SEy5KFz9ii/TZ5c/FoSrR+Xfsb8Bpnng6iH6WeHq Ufkw9X/sYepvQNXB1KPy78DVJYPN+YrBh5mHyudxgPFh/oHxYeEBALdOjD8= "]]& ], AspectRatio->NCache[Rational[10, 3]^Rational[1, 2], 1.8257418583505538`], FrameTicks->Automatic, ImageSize->{Automatic, 90}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "RightCrookedTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"RightCrookedTree[n] gives the n\[Hyphen]leaf path tree in \ which alternate vertices on successive levels have children, beginning with \ the right child.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571728-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"RightCrookedTree", "/@", RowBox[{"Range", "[", RowBox[{"2", ",", "10"}], "]"}]}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 0.8944271909999159}, {0., 0.}, {0.8944271909999159, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 10}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999159}, {0.8944271909999159, 0.8944271909999159}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 1.7888543819998317`}, { 0., 0.8944271909999159}, {0.8944271909999159, 0.8944271909999159}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.894427190999916}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 7}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 2.6832815729997477`}, { 0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.894427190999916}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999162}, {1.3416407864998738`, 2.683281572999748}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 11}, {4, 5}, {4, 6}, {6, 7}, {6, 10}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, {0.8944271909999159, 3.577708763999664}, { 0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999162}, {1.3416407864998738`, 2.683281572999748}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.6832815729997477`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, {1.3416407864998738`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 13}, {4, 5}, {4, 6}, {6, 7}, {6, 12}, {7, 8}, {7, 9}, {9, 10}, {9, 11}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.6832815729997477`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, {1.3416407864998738`, 3.577708763999664}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 6.260990336999411}, {0., 5.366563145999495}, {0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {0., 3.5777087639996634`}, { 0.8944271909999159, 3.5777087639996634`}, {0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998315`}, {0.8944271909999159, 1.7888543819998315`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}, { 1.3416407864998738`, 4.47213595499958}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 15}, {4, 5}, {4, 6}, {6, 7}, {6, 14}, {7, 8}, {7, 9}, {9, 10}, {9, 13}, {10, 11}, {10, 12}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 6.260990336999411}, {0., 5.366563145999495}, {0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {0., 3.5777087639996634`}, { 0.8944271909999159, 3.5777087639996634`}, {0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998315`}, {0.8944271909999159, 1.7888543819998315`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}, { 1.3416407864998738`, 4.47213595499958}}]& ], AspectRatio->NCache[2 Rational[2, 3]^Rational[1, 2], 1.632993161855452], FrameTicks->Automatic, ImageSize->{Automatic, 70}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 7.155417527999327}, {0., 6.260990336999411}, {0.8944271909999159, 6.260990336999411}, { 0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, { 0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997472`}, {0.8944271909999159, 2.6832815729997472`}, {0.4472135954999579, 1.7888543819998315`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.3416407864998738`, 1.7888543819998315`}, {1.3416407864998738`, 3.5777087639996634`}, {1.3416407864998738`, 5.366563145999495}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 17}, {4, 5}, {4, 6}, {6, 7}, {6, 16}, {7, 8}, {7, 9}, {9, 10}, {9, 15}, {10, 11}, {10, 12}, {12, 13}, {12, 14}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999495}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 7.155417527999327}, {0., 6.260990336999411}, {0.8944271909999159, 6.260990336999411}, { 0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, { 0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997472`}, {0.8944271909999159, 2.6832815729997472`}, {0.4472135954999579, 1.7888543819998315`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.3416407864998738`, 1.7888543819998315`}, {1.3416407864998738`, 3.5777087639996634`}, {1.3416407864998738`, 5.366563145999495}}]& ], AspectRatio->NCache[3^Rational[1, 2], 1.7320508075688772`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBmIQffPt/qOq8+/Yn/pqbd8qqeDAAAUQcRkHCP3GHpV/ x17uAzuvI7ckXH3SJ/+QmHJRuHpU/h37FV+mzy5/LAhXfwMszgNXj8q/A9XP iqb+jz2qehj/DpT/xp4BDdxEE08Gm/sVrh7Gh9kH48PcC+PD/AsAJxSIQA== "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 19}, {4, 5}, {4, 6}, {6, 7}, {6, 18}, {7, 8}, {7, 9}, {9, 10}, {9, 17}, {10, 11}, {10, 12}, {12, 13}, {12, 16}, {13, 14}, {13, 15}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGAQBmIQffPt/qOq8+/Yn/pqbd8qqeDAAAUQcRkHCP3GHpV/ x17uAzuvI7ckXH3SJ/+QmHJRuHpU/h37FV+mzy5/LAhXfwMszgNXj8q/A9XP iqb+jz2qehj/DpT/xp4BDdxEE08Gm/sVrh7Gh9kH48PcC+PD/AsAJxSIQA== "]]& ], AspectRatio->NCache[Rational[10, 3]^Rational[1, 2], 1.8257418583505538`], FrameTicks->Automatic, ImageSize->{Automatic, 90}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["LeftTurnTree", "Input"], StyleBox[" and ", "Text", FontWeight->"Plain"], StyleBox["RightTurnTree", "Input"] }], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "LeftTurnTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"LeftTurnTree[n1, n2, \[Ellipsis], nk] gives the (n1 + n2 + \ \[CenterEllipsis] + nk)\[Hyphen]leaf path tree made up of combs of length ni, \ beginning with a left comb.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571731-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "RightTurnTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"RightTurnTree[n1, n2, \[Ellipsis], nk] gives the (n1 + n2 + \ \[CenterEllipsis] + nk)\[Hyphen]leaf path tree made up of combs of length ni, \ beginning with a right comb.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571732-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Grid", "[", RowBox[{"Table", "[", RowBox[{ RowBox[{"BareTreeForm", "[", RowBox[{"LeftTurnTree", "[", RowBox[{"m", ",", "n"}], "]"}], "]"}], ",", RowBox[{"{", RowBox[{"m", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "2", ",", "7"}], "}"}]}], "]"}], "]"}]], "Input"], Cell[BoxData[ TagBox[GridBox[{ { GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999159}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999159}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 5}, {2, 3}, {2, 4}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999159}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999159}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999159}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999159}}]& ], AspectRatio->1, FrameTicks->Automatic, ImageSize->{Automatic, 20}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.894427190999916}, { 0.8944271909999159, 0.894427190999916}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 4}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.894427190999916}, { 0.8944271909999159, 0.894427190999916}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, { 6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {1.3416407864998738`, 1.788854381999832}, { 0.8944271909999159, 0.8944271909999162}, {1.7888543819998317`, 0.8944271909999162}, {1.3416407864998738`, 0.}, {2.23606797749979, 0.}, {1.3416407864998738`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, { 6, 8}, {8, 9}, {8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.577708763999664}, {0., 2.683281572999748}, { 0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {1.3416407864998738`, 1.788854381999832}, { 0.8944271909999159, 0.8944271909999162}, {1.7888543819998317`, 0.8944271909999162}, {1.3416407864998738`, 0.}, {2.23606797749979, 0.}, {1.3416407864998738`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {1.7888543819998317`, 1.788854381999832}, {1.3416407864998738`, 0.8944271909999157}, { 2.23606797749979, 0.8944271909999157}, {1.7888543819998317`, 0.}, { 2.6832815729997477`, 0.}, {1.3416407864998738`, 4.47213595499958}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 13}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, { 6, 8}, {8, 9}, {8, 10}, {10, 11}, {10, 12}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 5.366563145999495}, { 0.4472135954999579, 4.47213595499958}, {0., 3.577708763999664}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {1.7888543819998317`, 1.788854381999832}, {1.3416407864998738`, 0.8944271909999157}, { 2.23606797749979, 0.8944271909999157}, {1.7888543819998317`, 0.}, { 2.6832815729997477`, 0.}, {1.3416407864998738`, 4.47213595499958}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 6.260990336999411}, { 0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, { 0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, {1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {1.7888543819998317`, 2.6832815729997477`}, {1.3416407864998738`, 1.7888543819998315`}, { 2.23606797749979, 1.7888543819998315`}, {1.7888543819998317`, 0.8944271909999157}, {2.6832815729997477`, 0.8944271909999157}, { 2.23606797749979, 0.}, {3.1304951684997055`, 0.}, { 1.3416407864998738`, 5.366563145999495}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 15}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, { 6, 8}, {8, 9}, {8, 10}, {10, 11}, {10, 12}, {12, 13}, {12, 14}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999495}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 6.260990336999411}, { 0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, { 0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, {1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {1.7888543819998317`, 2.6832815729997477`}, {1.3416407864998738`, 1.7888543819998315`}, { 2.23606797749979, 1.7888543819998315`}, {1.7888543819998317`, 0.8944271909999157}, {2.6832815729997477`, 0.8944271909999157}, { 2.23606797749979, 0.}, {3.1304951684997055`, 0.}, { 1.3416407864998738`, 5.366563145999495}}]& ], AspectRatio->NCache[2 Rational[2, 3]^Rational[1, 2], 1.632993161855452], FrameTicks->Automatic, ImageSize->{Automatic, 70}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}, { GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.894427190999916}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.894427190999916}, {1.7888543819998317`, 1.788854381999832}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 7}, {2, 3}, {2, 6}, {3, 4}, {3, 5}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.894427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.894427190999916}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.894427190999916}, { 1.7888543819998317`, 1.788854381999832}}]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 30}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 5}, {5, 6}, { 5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 3.5777087639996634`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, { 1.3416407864998738`, 0.8944271909999162}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {1.3416407864998738`, 2.683281572999748}, {1.7888543819998317`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 10}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 4.47213595499958}, { 0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.683281572999748}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, {0.4472135954999579, 0.8944271909999162}, { 1.3416407864998738`, 0.8944271909999162}, {0.8944271909999159, 0.}, { 1.7888543819998317`, 0.}, {1.3416407864998738`, 2.683281572999748}, { 1.7888543819998317`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 5.366563145999495}, { 0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.577708763999664}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.788854381999832}, { 1.3416407864998738`, 1.788854381999832}, {0.8944271909999159, 0.8944271909999157}, {1.7888543819998317`, 0.8944271909999157}, { 1.3416407864998738`, 0.}, {2.23606797749979, 0.}, { 1.3416407864998738`, 3.577708763999664}, {1.7888543819998317`, 4.47213595499958}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 13}, {2, 3}, {2, 12}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 4.47213595499958}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 5.366563145999495}, { 0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.577708763999664}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.788854381999832}, { 1.3416407864998738`, 1.788854381999832}, {0.8944271909999159, 0.8944271909999157}, {1.7888543819998317`, 0.8944271909999157}, { 1.3416407864998738`, 0.}, {2.23606797749979, 0.}, { 1.3416407864998738`, 3.577708763999664}, {1.7888543819998317`, 4.47213595499958}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 6.260990336999411}, { 0.8944271909999159, 5.366563145999495}, {0.4472135954999579, 4.47213595499958}, {0., 3.5777087639996634`}, {0.8944271909999159, 3.5777087639996634`}, {0.4472135954999579, 2.6832815729997477`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998315`}, {1.7888543819998317`, 1.7888543819998315`}, { 1.3416407864998738`, 0.8944271909999157}, {2.23606797749979, 0.8944271909999157}, {1.7888543819998317`, 0.}, { 2.6832815729997477`, 0.}, {1.3416407864998738`, 4.47213595499958}, { 1.7888543819998317`, 5.366563145999495}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 15}, {2, 3}, {2, 14}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 13}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.366563145999495}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 6.260990336999411}, { 0.8944271909999159, 5.366563145999495}, {0.4472135954999579, 4.47213595499958}, {0., 3.5777087639996634`}, {0.8944271909999159, 3.5777087639996634`}, {0.4472135954999579, 2.6832815729997477`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998315`}, {1.7888543819998317`, 1.7888543819998315`}, { 1.3416407864998738`, 0.8944271909999157}, {2.23606797749979, 0.8944271909999157}, {1.7888543819998317`, 0.}, {2.6832815729997477`, 0.}, {1.3416407864998738`, 4.47213595499958}, {1.7888543819998317`, 5.366563145999495}}]& ], AspectRatio->NCache[2 Rational[2, 3]^Rational[1, 2], 1.632993161855452], FrameTicks->Automatic, ImageSize->{Automatic, 70}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 7.155417527999327}, { 0.8944271909999159, 6.260990336999411}, {0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, { 1.3416407864998738`, 3.5777087639996634`}, {0.8944271909999159, 2.6832815729997472`}, {1.7888543819998317`, 2.6832815729997472`}, { 1.3416407864998738`, 1.7888543819998315`}, {2.23606797749979, 1.7888543819998315`}, {1.7888543819998317`, 0.8944271909999157}, { 2.6832815729997477`, 0.8944271909999157}, {2.23606797749979, 0.}, { 3.1304951684997055`, 0.}, {1.3416407864998738`, 5.366563145999495}, {1.7888543819998317`, 6.260990336999411}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 17}, {2, 3}, {2, 16}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 13}, {13, 14}, {13, 15}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 6.260990336999411}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 7.155417527999327}, { 0.8944271909999159, 6.260990336999411}, {0.4472135954999579, 5.366563145999495}, {0., 4.47213595499958}, {0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, { 1.3416407864998738`, 3.5777087639996634`}, {0.8944271909999159, 2.6832815729997472`}, {1.7888543819998317`, 2.6832815729997472`}, { 1.3416407864998738`, 1.7888543819998315`}, {2.23606797749979, 1.7888543819998315`}, {1.7888543819998317`, 0.8944271909999157}, { 2.6832815729997477`, 0.8944271909999157}, {2.23606797749979, 0.}, { 3.1304951684997055`, 0.}, {1.3416407864998738`, 5.366563145999495}, { 1.7888543819998317`, 6.260990336999411}}]& ], AspectRatio->NCache[3^Rational[1, 2], 1.7320508075688772`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}, { GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 7}, {4, 5}, { 4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 3.5777087639996634`}, {1.3416407864998738`, 2.6832815729997477`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, {2.23606797749979, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 4.47213595499958}, { 1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, {0.8944271909999159, 0.8944271909999162}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.3416407864998738`, 1.788854381999832}, {1.7888543819998317`, 2.683281572999748}, {2.23606797749979, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 10}, {3, 4}, {3, 9}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 4.47213595499958}, { 1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.683281572999748}, {0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999162}, {0.8944271909999159, 0.8944271909999162}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.3416407864998738`, 1.788854381999832}, {1.7888543819998317`, 2.683281572999748}, {2.23606797749979, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 5.366563145999495}, { 1.3416407864998738`, 4.47213595499958}, {0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {1.3416407864998738`, 2.6832815729997477`}, { 1.7888543819998317`, 3.577708763999664}, {2.23606797749979, 4.47213595499958}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 13}, {2, 3}, {2, 12}, {3, 4}, {3, 11}, {4, 5}, {4, 6}, {6, 7}, {6, 8}, {8, 9}, {8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 5.366563145999495}, { 1.3416407864998738`, 4.47213595499958}, {0.8944271909999159, 3.577708763999664}, {0.4472135954999579, 2.6832815729997477`}, {0., 1.788854381999832}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {1.3416407864998738`, 2.6832815729997477`}, { 1.7888543819998317`, 3.577708763999664}, {2.23606797749979, 4.47213595499958}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 6.260990336999411}, { 1.3416407864998738`, 5.366563145999495}, {0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998315`}, {1.3416407864998738`, 1.7888543819998315`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, {2.23606797749979, 0.}, {1.3416407864998738`, 3.5777087639996634`}, {1.7888543819998317`, 4.47213595499958}, { 2.23606797749979, 5.366563145999495}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 15}, {2, 3}, {2, 14}, {3, 4}, {3, 13}, {4, 5}, {4, 6}, {6, 7}, {6, 8}, {8, 9}, {8, 10}, {10, 11}, {10, 12}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 5.366563145999495}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 6.260990336999411}, { 1.3416407864998738`, 5.366563145999495}, {0.8944271909999159, 4.47213595499958}, {0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998315`}, {1.3416407864998738`, 1.7888543819998315`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, {2.23606797749979, 0.}, {1.3416407864998738`, 3.5777087639996634`}, {1.7888543819998317`, 4.47213595499958}, { 2.23606797749979, 5.366563145999495}}]& ], AspectRatio->NCache[2 Rational[2, 3]^Rational[1, 2], 1.632993161855452], FrameTicks->Automatic, ImageSize->{Automatic, 70}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 7.155417527999327}, { 1.3416407864998738`, 6.260990336999411}, {0.8944271909999159, 5.366563145999495}, {0.4472135954999579, 4.47213595499958}, {0., 3.5777087639996634`}, {0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997472`}, {1.3416407864998738`, 2.6832815729997472`}, {0.8944271909999159, 1.7888543819998315`}, { 1.7888543819998317`, 1.7888543819998315`}, {1.3416407864998738`, 0.8944271909999157}, {2.23606797749979, 0.8944271909999157}, { 1.7888543819998317`, 0.}, {2.6832815729997477`, 0.}, { 1.3416407864998738`, 4.47213595499958}, {1.7888543819998317`, 5.366563145999495}, {2.23606797749979, 6.260990336999411}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 17}, {2, 3}, {2, 16}, {3, 4}, {3, 15}, {4, 5}, {4, 6}, {6, 7}, {6, 8}, {8, 9}, {8, 10}, {10, 11}, {10, 12}, { 12, 13}, {12, 14}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 6.260990336999411}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 7.155417527999327}, { 1.3416407864998738`, 6.260990336999411}, {0.8944271909999159, 5.366563145999495}, {0.4472135954999579, 4.47213595499958}, {0., 3.5777087639996634`}, {0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997472`}, {1.3416407864998738`, 2.6832815729997472`}, {0.8944271909999159, 1.7888543819998315`}, { 1.7888543819998317`, 1.7888543819998315`}, {1.3416407864998738`, 0.8944271909999157}, {2.23606797749979, 0.8944271909999157}, { 1.7888543819998317`, 0.}, {2.6832815729997477`, 0.}, { 1.3416407864998738`, 4.47213595499958}, {1.7888543819998317`, 5.366563145999495}, {2.23606797749979, 6.260990336999411}}]& ], AspectRatio->NCache[3^Rational[1, 2], 1.7320508075688772`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBmIQffPt/qOq8//Yn/pqbd8qqeCQ/Mk/JKb8qz1EXMYB Qr+xl/vAzuvILQnl37FPAqsTdWCAghVfps8ufywIV4/Kv2N/A0zzwM2H8WHq IeaxOsDcA+Ojqv8DNZfRAcaHqb8BNScZqu8GijsY4e6E+IMTzoeZD/MPzDyY f2H6YeEBAKOVlXk= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 19}, {2, 3}, {2, 18}, {3, 4}, {3, 17}, {4, 5}, {4, 6}, {6, 7}, {6, 8}, {8, 9}, {8, 10}, {10, 11}, {10, 12}, { 12, 13}, {12, 14}, {14, 15}, {14, 16}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 7.155417527999327}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGAQBmIQffPt/qOq8//Yn/pqbd8qqeCQ/Mk/JKb8qz1EXMYB Qr+xl/vAzuvILQnl37FPAqsTdWCAghVfps8ufywIV4/Kv2N/A0zzwM2H8WHq IeaxOsDcA+Ojqv8DNZfRAcaHqb8BNScZqu8GijsY4e6E+IMTzoeZD/MPzDyY f2H6YeEBAKOVlXk= "]]& ], AspectRatio->NCache[Rational[10, 3]^Rational[1, 2], 1.8257418583505538`], FrameTicks->Automatic, ImageSize->{Automatic, 90}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}, { GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, {1.7888543819998317`, 1.788854381999832}, { 2.23606797749979, 2.683281572999748}, {2.6832815729997477`, 3.577708763999664}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 11}, {2, 3}, {2, 10}, {3, 4}, {3, 9}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999162}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.577708763999664}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.577708763999664}, {1.3416407864998738`, 2.683281572999748}, {0.8944271909999159, 1.788854381999832}, { 0.4472135954999579, 0.8944271909999162}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999162}, { 1.7888543819998317`, 1.788854381999832}, {2.23606797749979, 2.683281572999748}, {2.6832815729997477`, 3.577708763999664}}]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 50}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{2.23606797749979, 5.366563145999495}, { 1.7888543819998317`, 4.47213595499958}, {1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, {1.7888543819998317`, 2.6832815729997477`}, { 2.23606797749979, 3.577708763999664}, {2.6832815729997477`, 4.47213595499958}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 13}, {2, 3}, {2, 12}, {3, 4}, {3, 11}, {4, 5}, {4, 10}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.788854381999832}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 4.47213595499958}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{2.23606797749979, 5.366563145999495}, { 1.7888543819998317`, 4.47213595499958}, {1.3416407864998738`, 3.577708763999664}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.788854381999832}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.788854381999832}, { 1.7888543819998317`, 2.6832815729997477`}, {2.23606797749979, 3.577708763999664}, {2.6832815729997477`, 4.47213595499958}}]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 60}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{2.23606797749979, 6.260990336999411}, { 1.7888543819998317`, 5.366563145999495}, {1.3416407864998738`, 4.47213595499958}, {0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998315`}, {0.8944271909999159, 1.7888543819998315`}, { 0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {1.3416407864998738`, 2.6832815729997477`}, { 1.7888543819998317`, 3.5777087639996634`}, {2.23606797749979, 4.47213595499958}, {2.6832815729997477`, 5.366563145999495}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 15}, {2, 3}, {2, 14}, {3, 4}, {3, 13}, {4, 5}, {4, 12}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 5.366563145999495}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{2.23606797749979, 6.260990336999411}, { 1.7888543819998317`, 5.366563145999495}, {1.3416407864998738`, 4.47213595499958}, {0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998315`}, {0.8944271909999159, 1.7888543819998315`}, { 0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, {0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, {1.3416407864998738`, 2.6832815729997477`}, { 1.7888543819998317`, 3.5777087639996634`}, {2.23606797749979, 4.47213595499958}, {2.6832815729997477`, 5.366563145999495}}]& ], AspectRatio->NCache[2 Rational[2, 3]^Rational[1, 2], 1.632993161855452], FrameTicks->Automatic, ImageSize->{Automatic, 70}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{2.23606797749979, 7.155417527999327}, { 1.7888543819998317`, 6.260990336999411}, {1.3416407864998738`, 5.366563145999495}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997472`}, {0.8944271909999159, 2.6832815729997472`}, { 0.4472135954999579, 1.7888543819998315`}, {1.3416407864998738`, 1.7888543819998315`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, {2.23606797749979, 0.}, {1.3416407864998738`, 3.5777087639996634`}, {1.7888543819998317`, 4.47213595499958}, { 2.23606797749979, 5.366563145999495}, {2.6832815729997477`, 6.260990336999411}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 17}, {2, 3}, {2, 16}, {3, 4}, {3, 15}, {4, 5}, {4, 14}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, { 11, 12}, {11, 13}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 6.260990336999411}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{2.23606797749979, 7.155417527999327}, { 1.7888543819998317`, 6.260990336999411}, {1.3416407864998738`, 5.366563145999495}, {0.8944271909999159, 4.47213595499958}, { 0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997472`}, {0.8944271909999159, 2.6832815729997472`}, { 0.4472135954999579, 1.7888543819998315`}, {1.3416407864998738`, 1.7888543819998315`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, {2.23606797749979, 0.}, {1.3416407864998738`, 3.5777087639996634`}, {1.7888543819998317`, 4.47213595499958}, { 2.23606797749979, 5.366563145999495}, {2.6832815729997477`, 6.260990336999411}}]& ], AspectRatio->NCache[3^Rational[1, 2], 1.7320508075688772`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBmIQveLL9NnljxkdTn21tm+VVHC4+Xb/UdX5f+whtIxD 8if/kJjyr/ZyH9h5HbklofJv7JPA4qJQ/h17iDmCDgxQcAMszgNXj8q/A9XP CjcfxkdVD3PHHzgfpv4GVB3M/TA+TD3MHclQc1H5X+HuhamH+QdmHsy/ySju knEAALZultI= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 19}, {2, 3}, {2, 18}, {3, 4}, {3, 17}, {4, 5}, {4, 16}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, { 11, 12}, {11, 13}, {13, 14}, {13, 15}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.577708763999663}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.3665631459994945`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 7.155417527999327}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGAQBmIQveLL9NnljxkdTn21tm+VVHC4+Xb/UdX5f+whtIxD 8if/kJjyr/ZyH9h5HbklofJv7JPA4qJQ/h17iDmCDgxQcAMszgNXj8q/A9XP CjcfxkdVD3PHHzgfpv4GVB3M/TA+TD3MHclQc1H5X+HuhamH+QdmHsy/ySju knEAALZultI= "]]& ], AspectRatio->NCache[Rational[10, 3]^Rational[1, 2], 1.8257418583505538`], FrameTicks->Automatic, ImageSize->{Automatic, 90}, PlotRange->All, PlotRangePadding->Scaled[0.1]], GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGAQBWIQveLL9NnljxkdILSiw823+4+qzv9jf+qrtX2rpIJD 8if/kJjyr/a3wOIyUPk39nIf2HkduSWh/Dv2KWB1og4MUAAxTxCuHpV/B2oe D5r5PHD1EPNY4e6B8WHq70DFYe6H8WHqH0DNSYbqe4DiDka4OyH+4ITzYebD /AMzD+ZfmH5YeMDMh4UXAOxCpNo= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 21}, {2, 3}, {2, 20}, {3, 4}, {3, 19}, {4, 5}, {4, 18}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, { 11, 12}, {11, 13}, {13, 14}, {13, 15}, {15, 16}, {15, 17}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.577708763999664}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998324`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 1.7888543819998324`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 8.049844718999243}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGAQBWIQveLL9NnljxkdILSiw823+4+qzv9jf+qrtX2rpIJD 8if/kJjyr/a3wOIyUPk39nIf2HkduSWh/Dv2KWB1og4MUAAxTxCuHpV/B2oe D5r5PHD1EPNY4e6B8WHq70DFYe6H8WHqH0DNSYbqe4DiDka4OyH+4ITzYebD /AMzD+ZfmH5YeMDMh4UXAOxCpNo= "]]& ], AspectRatio->NCache[Rational[11, 3]^Rational[1, 2], 1.9148542155126762`], FrameTicks->Automatic, ImageSize->{Automatic, 100}, PlotRange->All, PlotRangePadding->Scaled[0.1]]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["PathTree", "Input"], StyleBox[" and ", FontWeight->"Plain"], StyleBox["FromPathTree", "Input"] }], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "PathTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"PathTree[tuple] gives the path tree corresponding to a \ {0,1}-tuple.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571737-7342872"] }, Open ]], Cell["'0' means 'left', and '1' means 'right':", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "[", RowBox[{"PathTree", "[", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0"}], "}"}], "]"}], "]"}]], "Input"], Cell[BoxData[ GraphicsBox[ TagBox[GraphicsGroupBox[{ GraphicsComplexBox[{{3.5777087639996634`, 7.155417527999327}, { 3.1304951684997055`, 6.260990336999411}, {2.6832815729997477`, 5.366563145999495}, {2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.5777087639996634`}, {1.3416407864998738`, 2.6832815729997472`}, {0.8944271909999159, 1.7888543819998315`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998315`}, {2.23606797749979, 2.6832815729997472`}, { 2.6832815729997477`, 3.5777087639996634`}, {3.1304951684997055`, 4.47213595499958}, {3.5777087639996634`, 5.366563145999495}, { 4.024922359499621, 6.260990336999411}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 17}, {2, 3}, {2, 16}, {3, 4}, {3, 15}, {4, 5}, {4, 14}, {5, 6}, {5, 13}, {6, 7}, {6, 12}, {7, 8}, {7, 11}, {8, 9}, {8, 10}}]}], { {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 7.155417527999327}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998315`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997472`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 5.366563145999495}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 6.260990336999411}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{3.5777087639996634`, 7.155417527999327}, { 3.1304951684997055`, 6.260990336999411}, {2.6832815729997477`, 5.366563145999495}, {2.23606797749979, 4.47213595499958}, { 1.7888543819998317`, 3.5777087639996634`}, {1.3416407864998738`, 2.6832815729997472`}, {0.8944271909999159, 1.7888543819998315`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998315`}, {2.23606797749979, 2.6832815729997472`}, { 2.6832815729997477`, 3.5777087639996634`}, {3.1304951684997055`, 4.47213595499958}, {3.5777087639996634`, 5.366563145999495}, { 4.024922359499621, 6.260990336999411}}]& ], AspectRatio->NCache[3^Rational[1, 2], 1.7320508075688772`], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "FromPathTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"FromPathTree[pathtree] gives the {0,1}-tuple corresponding to \ a path tree.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571739-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"FromPathTree", "/@", RowBox[{"PathTrees", "[", "5", "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["PathTreeQ", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "PathTreeQ"}]], "Input"], Cell[BoxData[ StyleBox["\<\"PathTreeQ[expr] gives True if expr is a path tree, and False \ otherwise.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571744-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"Select", "[", RowBox[{ RowBox[{"BinaryTrees", "[", "5", "]"}], ",", "PathTreeQ"}], "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, { 1.7888543819998317`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 5}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 7}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["PathTrees", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "PathTrees"}]], "Input"], Cell[BoxData[ StyleBox["\<\"PathTrees[n] gives a list of all path trees with n \ leaves.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571747-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "/@", RowBox[{"PathTrees", "[", "5", "]"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 1.7888543819998317`, 0.8944271909999157}, {1.3416407864998738`, 0.}, { 2.23606797749979, 0.}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 9}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999157}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {1.3416407864998738`, 1.7888543819998317`}, {0.8944271909999159, 0.8944271909999157}, { 0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, { 1.7888543819998317`, 0.8944271909999157}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.4472135954999579, 3.5777087639996634`}, {0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.4472135954999579, 3.5777087639996634`}, { 0., 2.6832815729997477`}, {0.8944271909999159, 2.6832815729997477`}, { 0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, { 0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, { 1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, { 0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, { 1.7888543819998317`, 1.7888543819998317`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, { 0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, {6, 8}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {1.3416407864998738`, 0.8944271909999157}, { 0.8944271909999159, 0.}, {1.7888543819998317`, 0.}, { 1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 4}, {4, 5}, {4, 8}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{0.8944271909999159, 3.5777087639996634`}, { 0.4472135954999579, 2.6832815729997477`}, {0., 1.7888543819998317`}, { 0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, { 1.3416407864998738`, 0.8944271909999157}, {1.3416407864998738`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 5}, {5, 6}, {5, 7}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.3416407864998738`, 3.5777087639996634`}, { 0.8944271909999159, 2.6832815729997477`}, {0.4472135954999579, 1.7888543819998317`}, {0., 0.8944271909999157}, {0.8944271909999159, 0.8944271909999157}, {0.4472135954999579, 0.}, {1.3416407864998738`, 0.}, {1.3416407864998738`, 1.7888543819998317`}, {1.7888543819998317`, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[ GraphicsGroupBox[{ GraphicsComplexBox[{{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}, {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 9}, {2, 3}, {2, 8}, {3, 4}, {3, 7}, {4, 5}, {4, 6}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996634`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.6832815729997477`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999157}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998317`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.6832815729997477`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> {{1.7888543819998317`, 3.5777087639996634`}, { 1.3416407864998738`, 2.6832815729997477`}, {0.8944271909999159, 1.7888543819998317`}, {0.4472135954999579, 0.8944271909999157}, {0., 0.}, {0.8944271909999159, 0.}, {1.3416407864998738`, 0.8944271909999157}, {1.7888543819998317`, 1.7888543819998317`}, { 2.23606797749979, 2.6832815729997477`}}]& ], AspectRatio->NCache[Rational[5, 3]^Rational[1, 2], 1.2909944487358056`], FrameTicks->Automatic, ImageSize->{Automatic, 40}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["RandomBinaryTree", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "RandomBinaryTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"RandomBinaryTree[n] gives a pseudorandom binary tree with n \ leaves.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571748-7342872"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"BareTreeForm", "[", RowBox[{"RandomBinaryTree", "[", "20", "]"}], "]"}], ",", RowBox[{"{", "10", "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQve9ou6DzGwGHc0suP17nJe7wSGyqm8F7PgcTg0j2 yEQRB6a+E3OiZP/az9p9T4u5QhCq7rs9I1ic12E2WPyjPUScHSp/Haqe0YEB Cs5A9UHkn9vD+KjmM8LNh8nPhoqjq78ANQfiThYHGB8mD3MPTD/MvYmfk+bf XC7uAPOP6E7VjXrGYnD5dboLeltkJDHUw8zjm2w1gXm5sAPMvX6NC20imAXg 7suQ9DvAYsIFdw9MHywcmKDmwvgvvkpLrnsjBFc/G+oumDwsHmB8WDzB7GvM mvaV+ZooXL/0fYFLkfsl4Pytwd3r1q+QhrsX4j4ptPCUhfNh6mH6YepR3S8L 5/ufYO1mnSQHV/87/W61/kQpeHhxMxz9/zZBCJ6eAMpcEEM= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 16}, {3, 4}, {3, 15}, {4, 5}, { 4, 14}, {5, 6}, {5, 9}, {6, 7}, {6, 8}, {9, 10}, {9, 11}, {11, 12}, {11, 13}, {16, 17}, {16, 18}, {18, 19}, {18, 38}, {19, 20}, { 19, 31}, {20, 21}, {20, 28}, {21, 22}, {21, 25}, {22, 23}, {22, 24}, {25, 26}, {25, 27}, {28, 29}, {28, 30}, {31, 32}, {31, 33}, { 33, 34}, {33, 37}, {34, 35}, {34, 36}}]}], { {RGBColor[0, 0, 0.7], PointBox[{4.230724595939533, 5.8229327772070985`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.866791297364089, 5.095066180056211}]}, {RGBColor[0, 0, 0.7], PointBox[{1.8196664928772184`, 4.367199582905323}]}, {RGBColor[0, 0, 0.7], PointBox[{1.4557331943017746`, 3.6393329857544363`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.091799895726331, 2.9114663886035492`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.36393329857544365`, 2.1835997914526617`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.4557331943017742`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7278665971508873, 1.4557331943017742`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.8196664928772184`, 2.1835997914526617`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.4557331943017746`, 1.4557331943017742`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.183599791452662, 1.4557331943017742`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.8196664928772184`, 0.7278665971508875}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5475330900281055`, 0.7278665971508875}]}, {RGBColor[0, 0, 0.7], PointBox[{1.8196664928772184`, 2.9114663886035492`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.183599791452662, 3.6393329857544363`}]}, {RGBColor[0, 0, 0.7], PointBox[{5.913916101850959, 4.367199582905323}]}, {RGBColor[0, 0, 0.7], PointBox[{5.549982803275516, 3.6393329857544363`}]}, {RGBColor[0, 0, 0.7], PointBox[{6.277849400426403, 3.6393329857544363`}]}, {RGBColor[0, 0, 0.7], PointBox[{5.913916101850959, 2.9114663886035492`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.9130995307684895`, 2.1835997914526617`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.0032662843298805`, 1.4557331943017742`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.275399687178993, 0.7278665971508875}]}, {RGBColor[0, 0, 0.7], PointBox[{2.9114663886035492`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.6393329857544368`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.731132881480768, 0.7278665971508875}]}, {RGBColor[0, 0, 0.7], PointBox[{4.367199582905324, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{5.095066180056211, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{5.8229327772070985`, 1.4557331943017742`}]}, {RGBColor[0, 0, 0.7], PointBox[{5.458999478631655, 0.7278665971508875}]}, {RGBColor[0, 0, 0.7], PointBox[{6.186866075782542, 0.7278665971508875}]}, {RGBColor[0, 0, 0.7], PointBox[{6.91473267293343, 2.1835997914526617`}]}, {RGBColor[0, 0, 0.7], PointBox[{6.550799374357986, 1.4557331943017742`}]}, {RGBColor[0, 0, 0.7], PointBox[{7.2786659715088735`, 1.4557331943017742`}]}, {RGBColor[0, 0, 0.7], PointBox[{6.91473267293343, 0.7278665971508875}]}, {RGBColor[0, 0, 0.7], PointBox[{6.550799374357986, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{7.2786659715088735`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{7.642599270084317, 0.7278665971508875}]}, {RGBColor[0, 0, 0.7], PointBox[{6.641782699001847, 2.9114663886035492`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.5946578945149765`, 5.095066180056211}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQve9ou6DzGwGHc0suP17nJe7wSGyqm8F7PgcTg0j2 yEQRB6a+E3OiZP/az9p9T4u5QhCq7rs9I1ic12E2WPyjPUScHSp/Haqe0YEB Cs5A9UHkn9vD+KjmM8LNh8nPhoqjq78ANQfiThYHGB8mD3MPTD/MvYmfk+bf XC7uAPOP6E7VjXrGYnD5dboLeltkJDHUw8zjm2w1gXm5sAPMvX6NC20imAXg 7suQ9DvAYsIFdw9MHywcmKDmwvgvvkpLrnsjBFc/G+oumDwsHmB8WDzB7GvM mvaV+ZooXL/0fYFLkfsl4Pytwd3r1q+QhrsX4j4ptPCUhfNh6mH6YepR3S8L 5/ufYO1mnSQHV/87/W61/kQpeHhxMxz9/zZBCJ6eAMpcEEM= "]]& ], AspectRatio->NCache[Rational[1, 2] 3^Rational[1, 2], 0.8660254037844386], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQrVFwI/KdwW97RYaemq0zxRwUCrb+auj6ai/b8OtM 3TFhB4kdtXfWZjM4wPhKYHXX7CUZMmU9Pgs4MECBJsP620oOPFD5Z/ao/GtQ 89kcIPo+wPk6HzI5VVn4HGDmQWgGB5h+LTD9B64eYt43ewmoOph6GB+mXgGq Tg7sbmYHGB+mXgHqTph6mD9g6mF8Jai9MPUweZh7IOElCnev3IY3i54qiMDl lQzqgmS+iMH5MgpiihsFheHu1Wtw6I4U5oe7TwtqDsw+tQZZnTc5nHD3wNTD +LBwg6mHxyOK/4Xh8tIHDEsfxwjB9Ss4HFaRMhCF8yH2ScLVqxwIuRLALAGX 13B41tx+TQqDD/MPqn6Yf2TgfACE5dFV "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 9}, {4, 5}, {4, 6}, {6, 7}, {6, 8}, {9, 10}, {9, 21}, {10, 11}, {10, 20}, {11, 12}, {11, 13}, {13, 14}, {13, 15}, {15, 16}, {15, 19}, {16, 17}, {16, 18}, {21, 22}, { 21, 23}, {23, 24}, {23, 37}, {24, 25}, {24, 30}, {25, 26}, {25, 29}, {26, 27}, {26, 28}, {30, 31}, {30, 34}, {31, 32}, {31, 33}, { 34, 35}, {34, 36}, {37, 38}, {37, 39}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.6994460591877303`, 5.650106378598168}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3463144105253448`, 4.943843081273397}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0525777078501157`, 4.943843081273397}]}, {RGBColor[0, 0, 0.7], PointBox[{0.35313164866238556`, 4.237579783948626}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.531316486623855}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7062632973247711, 3.531316486623855}]}, {RGBColor[0, 0, 0.7], PointBox[{0.35313164866238556`, 2.825053189299084}]}, {RGBColor[0, 0, 0.7], PointBox[{1.0593949459871566`, 2.825053189299084}]}, {RGBColor[0, 0, 0.7], PointBox[{3.752023767037846, 4.237579783948626}]}, {RGBColor[0, 0, 0.7], PointBox[{2.118789891974313, 3.531316486623855}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7656582433119277`, 2.825053189299084}]}, {RGBColor[0, 0, 0.7], PointBox[{1.4125265946495422`, 2.1187898919743127`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.118789891974313, 2.1187898919743127`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7656582433119277`, 1.4125265946495418`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.471921540636699, 1.4125265946495418`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.118789891974313, 0.7062632973247709}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7656582433119277`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.471921540636699, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.8250531892990844`, 0.7062632973247709}]}, {RGBColor[0, 0, 0.7], PointBox[{2.471921540636699, 2.825053189299084}]}, {RGBColor[0, 0, 0.7], PointBox[{5.385257642101379, 3.531316486623855}]}, {RGBColor[0, 0, 0.7], PointBox[{5.032125993438994, 2.825053189299084}]}, {RGBColor[0, 0, 0.7], PointBox[{5.738389290763765, 2.825053189299084}]}, {RGBColor[0, 0, 0.7], PointBox[{4.767277256942204, 2.1187898919743127`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.8844481352862408`, 1.4125265946495418`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5313164866238553`, 0.7062632973247709}]}, {RGBColor[0, 0, 0.7], PointBox[{3.17818483796147, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.8844481352862408`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.237579783948626, 0.7062632973247709}]}, {RGBColor[0, 0, 0.7], PointBox[{5.650106378598168, 1.4125265946495418`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.943843081273398, 0.7062632973247709}]}, {RGBColor[0, 0, 0.7], PointBox[{4.590711432611012, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{5.296974729935783, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{6.35636967592294, 0.7062632973247709}]}, {RGBColor[0, 0, 0.7], PointBox[{6.003238027260554, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{6.709501324585325, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{6.709501324585325, 2.1187898919743127`}]}, {RGBColor[0, 0, 0.7], PointBox[{6.35636967592294, 1.4125265946495418`}]}, {RGBColor[0, 0, 0.7], PointBox[{7.062632973247711, 1.4125265946495418`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQrVFwI/KdwW97RYaemq0zxRwUCrb+auj6ai/b8OtM 3TFhB4kdtXfWZjM4wPhKYHXX7CUZMmU9Pgs4MECBJsP620oOPFD5Z/ao/GtQ 89kcIPo+wPk6HzI5VVn4HGDmQWgGB5h+LTD9B64eYt43ewmoOph6GB+mXgGq Tg7sbmYHGB+mXgHqTph6mD9g6mF8Jai9MPUweZh7IOElCnev3IY3i54qiMDl lQzqgmS+iMH5MgpiihsFheHu1Wtw6I4U5oe7TwtqDsw+tQZZnTc5nHD3wNTD +LBwg6mHxyOK/4Xh8tIHDEsfxwjB9Ss4HFaRMhCF8yH2ScLVqxwIuRLALAGX 13B41tx+TQqDD/MPqn6Yf2TgfACE5dFV "]]& ], AspectRatio->NCache[3 10^Rational[-1, 2], 0.9486832980505138], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQXcEWsq1krYBD2xat7GuZklCa0+Fr7NG5s23EHFLY Ey4k8DNDaWGH5YlfWX2O/LdfAab5oep/2sP0QdR9tk+F6oOI37TvgKpjgAII /yVU30t7GB9mfgeKuT/h8jD3oKtPRXEnM5o/2Bxg7l0OpWH+EeOeYCE4nQcu LxOzNvNwhSCcv3aTkPm/pSJo4SEMp9HFYeph+m05K1gsL4vD+TD1MPehhztM Pcw/BzayyQq5CDnAwiN+m9P8dbp8cP+fi797sZiB2wEWrrD4hPEDOXJe+RSK wtVzxO5sXn9LGC4/c7Nc4Ct2cTh/V8LL1/FJsnD7iraatR46LQ3Xr8XVIqdq KoWhHsZn5pkT9PeHHJr7pOH+AQCaRPFH "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 19}, {2, 3}, {2, 16}, {3, 4}, {3, 15}, {4, 5}, { 4, 14}, {5, 6}, {5, 13}, {6, 7}, {6, 10}, {7, 8}, {7, 9}, {10, 11}, {10, 12}, {16, 17}, {16, 18}, {19, 20}, {19, 21}, {21, 22}, { 21, 23}, {23, 24}, {23, 25}, {25, 26}, {25, 39}, {26, 27}, {26, 34}, {27, 28}, {27, 31}, {28, 29}, {28, 30}, {31, 32}, {31, 33}, { 34, 35}, {34, 38}, {35, 36}, {35, 37}}]}], { {RGBColor[0, 0, 0.7], PointBox[{4.169390534285064, 6.3533570046248595`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1766785023124298`, 5.559187379046752}]}, {RGBColor[0, 0, 0.7], PointBox[{2.382508876734322, 4.765017753468644}]}, {RGBColor[0, 0, 0.7], PointBox[{1.9854240639452685`, 3.9708481278905374`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.5883392511562149`, 3.1766785023124298`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.191254438367161, 2.3825088767343225`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.3970848127890537, 1.5883392511562153`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.7941696255781077}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7941696255781074, 0.7941696255781077}]}, {RGBColor[0, 0, 0.7], PointBox[{1.9854240639452685`, 1.5883392511562153`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.5883392511562149`, 0.7941696255781077}]}, {RGBColor[0, 0, 0.7], PointBox[{2.382508876734322, 0.7941696255781077}]}, {RGBColor[0, 0, 0.7], PointBox[{1.9854240639452685`, 2.3825088767343225`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.382508876734322, 3.1766785023124298`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.779593689523376, 3.9708481278905374`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.970848127890537, 4.765017753468644}]}, {RGBColor[0, 0, 0.7], PointBox[{3.573763315101483, 3.9708481278905374`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.367932940679591, 3.9708481278905374`}]}, {RGBColor[0, 0, 0.7], PointBox[{5.1621025662576985`, 5.559187379046752}]}, {RGBColor[0, 0, 0.7], PointBox[{4.765017753468644, 4.765017753468644}]}, {RGBColor[0, 0, 0.7], PointBox[{5.559187379046752, 4.765017753468644}]}, {RGBColor[0, 0, 0.7], PointBox[{5.1621025662576985`, 3.9708481278905374`}]}, {RGBColor[0, 0, 0.7], PointBox[{5.956272191835805, 3.9708481278905374`}]}, {RGBColor[0, 0, 0.7], PointBox[{5.559187379046752, 3.1766785023124298`}]}, {RGBColor[0, 0, 0.7], PointBox[{6.3533570046248595`, 3.1766785023124298`}]}, {RGBColor[0, 0, 0.7], PointBox[{5.956272191835805, 2.3825088767343225`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.5664753470741175`, 1.5883392511562153`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.7723057214960103`, 0.7941696255781077}]}, {RGBColor[0, 0, 0.7], PointBox[{3.3752209087069565`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.169390534285064, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{5.360644972652225, 0.7941696255781077}]}, {RGBColor[0, 0, 0.7], PointBox[{4.963560159863171, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{5.757729785441279, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{7.346069036597493, 1.5883392511562153`}]}, {RGBColor[0, 0, 0.7], PointBox[{6.94898422380844, 0.7941696255781077}]}, {RGBColor[0, 0, 0.7], PointBox[{6.551899411019386, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{7.346069036597493, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{7.743153849386547, 0.7941696255781077}]}, {RGBColor[0, 0, 0.7], PointBox[{6.750441817413913, 2.3825088767343225`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQXcEWsq1krYBD2xat7GuZklCa0+Fr7NG5s23EHFLY Ey4k8DNDaWGH5YlfWX2O/LdfAab5oep/2sP0QdR9tk+F6oOI37TvgKpjgAII /yVU30t7GB9mfgeKuT/h8jD3oKtPRXEnM5o/2Bxg7l0OpWH+EeOeYCE4nQcu LxOzNvNwhSCcv3aTkPm/pSJo4SEMp9HFYeph+m05K1gsL4vD+TD1MPehhztM Pcw/BzayyQq5CDnAwiN+m9P8dbp8cP+fi797sZiB2wEWrrD4hPEDOXJe+RSK wtVzxO5sXn9LGC4/c7Nc4Ct2cTh/V8LL1/FJsnD7iraatR46LQ3Xr8XVIqdq KoWhHsZn5pkT9PeHHJr7pOH+AQCaRPFH "]]& ], AspectRatio->NCache[3 11^Rational[-1, 2], 0.9045340337332909], FrameTicks->Automatic, ImageSize->{Automatic, 80}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ/cqnh6ujgtehLWCmluZ1BQceri/3uJWZHdat3JlS OU8OSr+zD9jkULKgT9rB9MzVRaLxj+w/7TrefLxOwmHyYb/J7/K+wvkQ+ob9 FLC4qAMDFED0CTl8BMu/sIfxITSTA0w9RP8PNPlP9hB38MH1Q9RxwO0zg5oD Uw/jw+S/QM2FuecD1ByYeR9QzL1hj+ruT3A+xB3/4ObB3PsBxV9MDqjm/YC7 F6Yf1T8cDjD/QsKT1QEm7w8Od24HdPUw89ZCxWF8mHqY/yHxKgDnw9TD4hOm HhZ/MPNh8QFTD+PDzIOpf+IuJM30XBieXmD+gJk/GaoPxgcAA0EyJQ== "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 37}, {2, 3}, {2, 32}, {3, 4}, {3, 5}, {5, 6}, { 5, 9}, {6, 7}, {6, 8}, {9, 10}, {9, 25}, {10, 11}, {10, 24}, {11, 12}, {11, 23}, {12, 13}, {12, 14}, {14, 15}, {14, 20}, {15, 16}, { 15, 17}, {17, 18}, {17, 19}, {20, 21}, {20, 22}, {25, 26}, {25, 27}, {27, 28}, {27, 29}, {29, 30}, {29, 31}, {32, 33}, {32, 36}, { 33, 34}, {33, 35}, {37, 38}, {37, 39}}]}], { {RGBColor[0, 0, 0.7], PointBox[{3.683853228003149, 8.420235949721484}]}, {RGBColor[0, 0, 0.7], PointBox[{2.3921124857163303`, 7.654759954292258}]}, {RGBColor[0, 0, 0.7], PointBox[{0.9568449942865322, 6.889283958863032}]}, {RGBColor[0, 0, 0.7], PointBox[{0.5741069965719193, 6.123807963433807}]}, {RGBColor[0, 0, 0.7], PointBox[{1.339582992001145, 6.123807963433807}]}, {RGBColor[0, 0, 0.7], PointBox[{0.3827379977146129, 5.358331968004581}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 4.592855972575355}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7654759954292257, 4.592855972575355}]}, {RGBColor[0, 0, 0.7], PointBox[{2.2964279862876773`, 5.358331968004581}]}, {RGBColor[0, 0, 0.7], PointBox[{1.5309519908584517`, 4.592855972575355}]}, {RGBColor[0, 0, 0.7], PointBox[{1.1482139931438387`, 3.827379977146129}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7654759954292257, 3.0619039817169034`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.3827379977146129, 2.2964279862876777`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.1482139931438387`, 2.2964279862876777`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.3827379977146129, 1.5309519908584521`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.7654759954292256}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7654759954292257, 0.7654759954292256}]}, {RGBColor[0, 0, 0.7], PointBox[{0.3827379977146129, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.1482139931438387`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.9136899885730645`, 1.5309519908584521`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.5309519908584517`, 0.7654759954292256}]}, {RGBColor[0, 0, 0.7], PointBox[{2.2964279862876773`, 0.7654759954292256}]}, {RGBColor[0, 0, 0.7], PointBox[{1.5309519908584517`, 3.0619039817169034`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.9136899885730645`, 3.827379977146129}]}, {RGBColor[0, 0, 0.7], PointBox[{3.061903981716903, 4.592855972575355}]}, {RGBColor[0, 0, 0.7], PointBox[{2.67916598400229, 3.827379977146129}]}, {RGBColor[0, 0, 0.7], PointBox[{3.4446419794315157`, 3.827379977146129}]}, {RGBColor[0, 0, 0.7], PointBox[{3.061903981716903, 3.0619039817169034`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.8273799771461285`, 3.0619039817169034`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.4446419794315157`, 2.2964279862876777`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.210117974860742, 2.2964279862876777`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.8273799771461285`, 6.889283958863032}]}, {RGBColor[0, 0, 0.7], PointBox[{3.4446419794315157`, 6.123807963433807}]}, {RGBColor[0, 0, 0.7], PointBox[{3.061903981716903, 5.358331968004581}]}, {RGBColor[0, 0, 0.7], PointBox[{3.8273799771461285`, 5.358331968004581}]}, {RGBColor[0, 0, 0.7], PointBox[{4.210117974860742, 6.123807963433807}]}, {RGBColor[0, 0, 0.7], PointBox[{4.975593970289967, 7.654759954292258}]}, {RGBColor[0, 0, 0.7], PointBox[{4.592855972575355, 6.889283958863032}]}, {RGBColor[0, 0, 0.7], PointBox[{5.35833196800458, 6.889283958863032}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ/cqnh6ujgtehLWCmluZ1BQceri/3uJWZHdat3JlS OU8OSr+zD9jkULKgT9rB9MzVRaLxj+w/7TrefLxOwmHyYb/J7/K+wvkQ+ob9 FLC4qAMDFED0CTl8BMu/sIfxITSTA0w9RP8PNPlP9hB38MH1Q9RxwO0zg5oD Uw/jw+S/QM2FuecD1ByYeR9QzL1hj+ruT3A+xB3/4ObB3PsBxV9MDqjm/YC7 F6Yf1T8cDjD/QsKT1QEm7w8Od24HdPUw89ZCxWF8mHqY/yHxKgDnw9TD4hOm HhZ/MPNh8QFTD+PDzIOpf+IuJM30XBieXmD+gJk/GaoPxgcAA0EyJQ== "]]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 110}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ3SPWen0ur6CD+uu3E3hkVR3myDQ/X3+bz+FlktZa t1plh8W/SyJmxHA4rL6VdrLhriJUHatDbtDip7tsFRzkef7Iq8zhhvNh8nFT 9jO/spaF6mN0eNhsYRP3R9LhEZh+aZ9avLHk0h4xhwdg/k17iH3CUHs/w/kw eYj5Ag4MUAAxhxNuHowPUcfgAFMPsfcnXB5iLrMDjA9xJ68DzD0PUdQJw82B 8WHqUc3ndEC1XwDD/BdQeyHhIQjnw9Q/gLoTpv4B1F8w82H+Rg8HmHkw9ajh 9tMeJg/TB4tPWHzA4h8WX7D4h8mfmuexO3mtEAYflh5g+mHxz6HOM1/TVwTO h6mHpScA9mIO+g== "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 36}, {3, 4}, {3, 5}, {5, 6}, { 5, 33}, {6, 7}, {6, 32}, {7, 8}, {7, 17}, {8, 9}, {8, 10}, {10, 11}, {10, 14}, {11, 12}, {11, 13}, {14, 15}, {14, 16}, {17, 18}, { 17, 19}, {19, 20}, {19, 31}, {20, 21}, {20, 22}, {22, 23}, {22, 24}, {24, 25}, {24, 30}, {25, 26}, {25, 29}, {26, 27}, {26, 28}, { 33, 34}, {33, 35}, {36, 37}, {36, 38}}]}], { {RGBColor[0, 0, 0.7], PointBox[{4.263297431467105, 10.556736496966165`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.8572691046607144`, 9.744679843353383}]}, {RGBColor[0, 0, 0.7], PointBox[{3.045212451047932, 8.932623189740601}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6391841242415413`, 8.12056653612782}]}, {RGBColor[0, 0, 0.7], PointBox[{3.451240777854323, 8.12056653612782}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6391841242415413`, 7.308509882515038}]}, {RGBColor[0, 0, 0.7], PointBox[{2.2331557974351504`, 6.496453228902255}]}, {RGBColor[0, 0, 0.7], PointBox[{0.812056653612782, 5.684396575289473}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4060283268063909, 4.872339921676692}]}, {RGBColor[0, 0, 0.7], PointBox[{1.218084980419173, 4.872339921676692}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4060283268063909, 4.06028326806391}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.248226614451128}]}, {RGBColor[0, 0, 0.7], PointBox[{0.812056653612782, 3.248226614451128}]}, {RGBColor[0, 0, 0.7], PointBox[{2.030141634031955, 4.06028326806391}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6241133072255638`, 3.248226614451128}]}, {RGBColor[0, 0, 0.7], PointBox[{2.436169960838346, 3.248226614451128}]}, {RGBColor[0, 0, 0.7], PointBox[{3.654254941257519, 5.684396575289473}]}, {RGBColor[0, 0, 0.7], PointBox[{3.2482266144511276`, 4.872339921676692}]}, {RGBColor[0, 0, 0.7], PointBox[{4.06028326806391, 4.872339921676692}]}, {RGBColor[0, 0, 0.7], PointBox[{3.654254941257519, 4.06028326806391}]}, {RGBColor[0, 0, 0.7], PointBox[{3.2482266144511276`, 3.248226614451128}]}, {RGBColor[0, 0, 0.7], PointBox[{4.06028326806391, 3.248226614451128}]}, {RGBColor[0, 0, 0.7], PointBox[{3.654254941257519, 2.4361699608383454`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.466311594870301, 2.4361699608383454`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.06028326806391, 1.6241133072255636`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.654254941257519, 0.8120566536127818}]}, {RGBColor[0, 0, 0.7], PointBox[{3.2482266144511276`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.06028326806391, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.466311594870301, 0.8120566536127818}]}, {RGBColor[0, 0, 0.7], PointBox[{4.872339921676692, 1.6241133072255636`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.466311594870301, 4.06028326806391}]}, {RGBColor[0, 0, 0.7], PointBox[{3.045212451047932, 6.496453228902255}]}, {RGBColor[0, 0, 0.7], PointBox[{4.263297431467105, 7.308509882515038}]}, {RGBColor[0, 0, 0.7], PointBox[{3.8572691046607144`, 6.496453228902255}]}, {RGBColor[0, 0, 0.7], PointBox[{4.669325758273496, 6.496453228902255}]}, {RGBColor[0, 0, 0.7], PointBox[{4.669325758273496, 8.932623189740601}]}, {RGBColor[0, 0, 0.7], PointBox[{4.263297431467105, 8.12056653612782}]}, {RGBColor[0, 0, 0.7], PointBox[{5.075354085079887, 8.12056653612782}]}, {RGBColor[0, 0, 0.7], PointBox[{4.669325758273496, 9.744679843353383}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ3SPWen0ur6CD+uu3E3hkVR3myDQ/X3+bz+FlktZa t1plh8W/SyJmxHA4rL6VdrLhriJUHatDbtDip7tsFRzkef7Iq8zhhvNh8nFT 9jO/spaF6mN0eNhsYRP3R9LhEZh+aZ9avLHk0h4xhwdg/k17iH3CUHs/w/kw eYj5Ag4MUAAxhxNuHowPUcfgAFMPsfcnXB5iLrMDjA9xJ68DzD0PUdQJw82B 8WHqUc3ndEC1XwDD/BdQeyHhIQjnw9Q/gLoTpv4B1F8w82H+Rg8HmHkw9ajh 9tMeJg/TB4tPWHzA4h8WX7D4h8mfmuexO3mtEAYflh5g+mHxz6HOM1/TVwTO h6mHpScA9mIO+g== "]]& ], AspectRatio->NCache[2^Rational[1, 2], 1.4142135623730951`], FrameTicks->Automatic, ImageSize->{Automatic, 130}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ7TBFkjdhHYNDVSfTisxIJYdZwf3rZm74ZQ8RV4Dy X9nz2SU+WcMmB+XfsofQUg4MUKCeubeiLUocrh7G31L32qmY5QtcPYTP4gAz D2Y/TB6ijx3Oh6j7BzcPQn+3h5gjAnU3kwOMD5OHmCsANf8D1H4uqLon9jB3 oJrHApefAQ0HiL5T9gug/oKZB+PD7Ieph7kXJv+2+MrdmvWsDujqYeGWGLdM eAIrJ5wP0w9zL0we5h+YeTD5Kx4VnoujeRzQ1cP8427sVb9tIz8GHxaeMP2w 8LvL13frSbMgnA9TD7NfnKW89J2eMJwPUw+zP/BnvMCPmyIOqOHN4gBLTwCH RQF1 "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 8}, {3, 4}, {3, 7}, {4, 5}, {4, 6}, {8, 9}, {8, 10}, {10, 11}, {10, 32}, {11, 12}, {11, 13}, {13, 14}, {13, 27}, {14, 15}, {14, 26}, {15, 16}, {15, 17}, {17, 18}, { 17, 21}, {18, 19}, {18, 20}, {21, 22}, {21, 23}, {23, 24}, {23, 25}, {27, 28}, {27, 29}, {29, 30}, {29, 31}, {32, 33}, {32, 34}, { 34, 35}, {34, 36}, {36, 37}, {36, 38}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 9.17463421851129}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6681153124565982`, 8.34057656228299}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 7.506518906054692}]}, {RGBColor[0, 0, 0.7], PointBox[{0.41702882811414954`, 6.672461249826393}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 5.838403593598094}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8340576562282991, 5.838403593598094}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2510864843424487`, 6.672461249826393}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 7.506518906054692}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0851441405707476`, 6.672461249826393}]}, {RGBColor[0, 0, 0.7], PointBox[{2.919201796799047, 6.672461249826393}]}, {RGBColor[0, 0, 0.7], PointBox[{1.876629726513673, 5.838403593598094}]}, {RGBColor[0, 0, 0.7], PointBox[{1.4596008983995234`, 5.004345937369795}]}, {RGBColor[0, 0, 0.7], PointBox[{2.2936585546278225`, 5.004345937369795}]}, {RGBColor[0, 0, 0.7], PointBox[{1.4596008983995234`, 4.170288281141495}]}, {RGBColor[0, 0, 0.7], PointBox[{1.0425720702853738`, 3.3362306249131963`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.6255432421712244, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.4596008983995234`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.6255432421712244, 1.6681153124565977`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.20851441405707477`, 0.8340576562282997}]}, {RGBColor[0, 0, 0.7], PointBox[{1.0425720702853738`, 0.8340576562282997}]}, {RGBColor[0, 0, 0.7], PointBox[{2.2936585546278225`, 1.6681153124565977`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.876629726513673, 0.8340576562282997}]}, {RGBColor[0, 0, 0.7], PointBox[{2.710687382741972, 0.8340576562282997}]}, {RGBColor[0, 0, 0.7], PointBox[{2.2936585546278225`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.127716210856122, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.876629726513673, 3.3362306249131963`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.127716210856122, 4.170288281141495}]}, {RGBColor[0, 0, 0.7], PointBox[{2.710687382741972, 3.3362306249131963`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5447450389702713`, 3.3362306249131963`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.127716210856122, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.9617738670844207`, 2.5021729686848975`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.9617738670844207`, 5.838403593598094}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5447450389702713`, 5.004345937369795}]}, {RGBColor[0, 0, 0.7], PointBox[{4.37880269519857, 5.004345937369795}]}, {RGBColor[0, 0, 0.7], PointBox[{3.9617738670844207`, 4.170288281141495}]}, {RGBColor[0, 0, 0.7], PointBox[{4.79583152331272, 4.170288281141495}]}, {RGBColor[0, 0, 0.7], PointBox[{4.37880269519857, 3.3362306249131963`}]}, {RGBColor[0, 0, 0.7], PointBox[{5.21286035142687, 3.3362306249131963`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5021729686848975`, 8.34057656228299}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ7TBFkjdhHYNDVSfTisxIJYdZwf3rZm74ZQ8RV4Dy X9nz2SU+WcMmB+XfsofQUg4MUKCeubeiLUocrh7G31L32qmY5QtcPYTP4gAz D2Y/TB6ijx3Oh6j7BzcPQn+3h5gjAnU3kwOMD5OHmCsANf8D1H4uqLon9jB3 oJrHApefAQ0HiL5T9gug/oKZB+PD7Ieph7kXJv+2+MrdmvWsDujqYeGWGLdM eAIrJ5wP0w9zL0we5h+YeTD5Kx4VnoujeRzQ1cP8427sVb9tIz8GHxaeMP2w 8LvL13frSbMgnA9TD7NfnKW89J2eMJwPUw+zP/BnvMCPmyIOqOHN4gBLTwCH RQF1 "]]& ], AspectRatio->NCache[Rational[3, 2]^Rational[1, 2], 1.224744871391589], FrameTicks->Automatic, ImageSize->{Automatic, 110}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ/WFpz4G8OFaHC2c9uo9elnO4K/d48/8JTA573ebX hbHJOOwB02/sV+3/WvjcQtKhUOun96wLD+xnWPikVmSLObRsXBTBOe8znM+d I3ciU4HPAaYeYu4/uPx0MP3MHqJP2GEamH/NvghsrgDU/A9wPkz9PrA7eODq IeaxwdXD+DD1EP0MaOq/2TNAwQyoOph6GB+mHqYOZj46H2bedCgNsw/Gh7kX Eg6cDjD/QmhmB1T/MjjA1E+H+gPGh4QfH1z9Xqg4TB4mjq4eFh6/3/peCjQX ckANHzEH1PgThtMw9TBz+Uq/3zvAIgrnw+IVpl7xz4LX+pfE4fLGzV4/5s2X gvOZdc3O3tXmgKcnALvXBoc= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 6}, {3, 4}, {3, 5}, {6, 7}, {6, 32}, {7, 8}, {7, 23}, {8, 9}, {8, 10}, {10, 11}, {10, 22}, {11, 12}, {11, 13}, {13, 14}, {13, 21}, {14, 15}, {14, 20}, {15, 16}, { 15, 17}, {17, 18}, {17, 19}, {23, 24}, {23, 27}, {24, 25}, {24, 26}, {27, 28}, {27, 29}, {29, 30}, {29, 31}, {32, 33}, {32, 36}, { 33, 34}, {33, 35}, {36, 37}, {36, 38}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.671109680454485, 7.706808258360482}]}, {RGBColor[0, 0, 0.7], PointBox[{2.3208002141653723`, 7.006189325782256}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8757736657227819, 6.305570393204031}]}, {RGBColor[0, 0, 0.7], PointBox[{0.5254641994336692, 5.604951460625806}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2260831320118948`, 5.604951460625806}]}, {RGBColor[0, 0, 0.7], PointBox[{3.7658267626079627`, 6.305570393204031}]}, {RGBColor[0, 0, 0.7], PointBox[{1.9267020645901205`, 5.604951460625806}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7006189325782256, 4.904332528047579}]}, {RGBColor[0, 0, 0.7], PointBox[{0.35030946628911275`, 4.203713595469354}]}, {RGBColor[0, 0, 0.7], PointBox[{1.0509283988673384`, 4.203713595469354}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7006189325782256, 3.5030946628911286`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.35030946628911275`, 2.802475730312903}]}, {RGBColor[0, 0, 0.7], PointBox[{1.0509283988673384`, 2.802475730312903}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7006189325782256, 2.101856797734677}]}, {RGBColor[0, 0, 0.7], PointBox[{0.35030946628911275`, 1.4012378651564514`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.7006189325782257}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7006189325782256, 0.7006189325782257}]}, {RGBColor[0, 0, 0.7], PointBox[{0.35030946628911275`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.0509283988673384`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.0509283988673384`, 1.4012378651564514`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.4012378651564512`, 2.101856797734677}]}, {RGBColor[0, 0, 0.7], PointBox[{1.4012378651564512`, 3.5030946628911286`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1527851966020153`, 4.904332528047579}]}, {RGBColor[0, 0, 0.7], PointBox[{2.4521662640237896`, 4.203713595469354}]}, {RGBColor[0, 0, 0.7], PointBox[{2.1018567977346767`, 3.5030946628911286`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.8024757303129024`, 3.5030946628911286`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.853404129180241, 4.203713595469354}]}, {RGBColor[0, 0, 0.7], PointBox[{3.503094662891128, 3.5030946628911286`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.203713595469354, 3.5030946628911286`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.853404129180241, 2.802475730312903}]}, {RGBColor[0, 0, 0.7], PointBox[{4.554023061758467, 2.802475730312903}]}, {RGBColor[0, 0, 0.7], PointBox[{5.604951460625805, 5.604951460625806}]}, {RGBColor[0, 0, 0.7], PointBox[{4.904332528047579, 4.904332528047579}]}, {RGBColor[0, 0, 0.7], PointBox[{4.554023061758467, 4.203713595469354}]}, {RGBColor[0, 0, 0.7], PointBox[{5.254641994336692, 4.203713595469354}]}, {RGBColor[0, 0, 0.7], PointBox[{6.305570393204031, 4.904332528047579}]}, {RGBColor[0, 0, 0.7], PointBox[{5.955260926914918, 4.203713595469354}]}, {RGBColor[0, 0, 0.7], PointBox[{6.655879859493143, 4.203713595469354}]}, {RGBColor[0, 0, 0.7], PointBox[{3.021419146743598, 7.006189325782256}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ/WFpz4G8OFaHC2c9uo9elnO4K/d48/8JTA573ebX hbHJOOwB02/sV+3/WvjcQtKhUOun96wLD+xnWPikVmSLObRsXBTBOe8znM+d I3ciU4HPAaYeYu4/uPx0MP3MHqJP2GEamH/NvghsrgDU/A9wPkz9PrA7eODq IeaxwdXD+DD1EP0MaOq/2TNAwQyoOph6GB+mHqYOZj46H2bedCgNsw/Gh7kX Eg6cDjD/QmhmB1T/MjjA1E+H+gPGh4QfH1z9Xqg4TB4mjq4eFh6/3/peCjQX ckANHzEH1PgThtMw9TBz+Uq/3zvAIgrnw+IVpl7xz4LX+pfE4fLGzV4/5s2X gvOZdc3O3tXmgKcnALvXBoc= "]]& ], AspectRatio->NCache[2 Rational[3, 11]^Rational[1, 2], 1.044465935734187], FrameTicks->Automatic, ImageSize->{Automatic, 110}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQbVK27M4j/w/2XkX+s22vqTnYf/llLTD5sb2r8dLX y0xUHSDi3+B8mLwDmFZ2CPmw+FeW5Cl7q60BPZUfFR1g5sH4MPWmYHEFuHkw PkT/Lfv4vB+RM2JkHRigIBQsLgWVf2UP40PMY3aAqYfI/0KT/wz1jxhcP8S9 wnD7IPYLwNXD+DD1EJoLbj4q/xbUPGa4eyNQ1L2yR+Xfsk+AijOggRA0cZh7 YOoh/mBzgNkH8z/MfIi7GRzQ1Seg+QPVPb/g4QHTjxpeXA6w8ISZB5OHhDsv nA+JZ0YHWHqIA8v/hcc/JN2wOsD4ADIVHPo= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 37}, {4, 5}, {4, 6}, {6, 7}, {6, 8}, {8, 9}, {8, 12}, {9, 10}, {9, 11}, {12, 13}, {12, 34}, {13, 14}, {13, 33}, {14, 15}, {14, 32}, {15, 16}, {15, 17}, {17, 18}, { 17, 19}, {19, 20}, {19, 27}, {20, 21}, {20, 22}, {22, 23}, {22, 26}, {23, 24}, {23, 25}, {27, 28}, {27, 31}, {28, 29}, {28, 30}, { 34, 35}, {34, 36}, {37, 38}, {37, 39}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.0195034617567105`, 11.41843877167516}]}, {RGBColor[0, 0, 0.7], PointBox[{0.6117020770540263, 10.602836002269791`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.427304846459395, 10.602836002269791`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.6117020770540263, 9.787233232864423}]}, {RGBColor[0, 0, 0.7], PointBox[{0.20390069235134212`, 8.971630463459054}]}, {RGBColor[0, 0, 0.7], PointBox[{1.0195034617567105`, 8.971630463459054}]}, {RGBColor[0, 0, 0.7], PointBox[{0.6117020770540263, 8.156027694053686}]}, {RGBColor[0, 0, 0.7], PointBox[{1.427304846459395, 8.156027694053686}]}, {RGBColor[0, 0, 0.7], PointBox[{0.40780138470268423`, 7.340424924648317}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 6.524822155242949}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8156027694053685, 6.524822155242949}]}, {RGBColor[0, 0, 0.7], PointBox[{2.4468083082161054`, 7.340424924648317}]}, {RGBColor[0, 0, 0.7], PointBox[{1.631205538810737, 6.524822155242949}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2234041541080527`, 5.70921938583758}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8156027694053685, 4.893616616432212}]}, {RGBColor[0, 0, 0.7], PointBox[{0.40780138470268423`, 4.078013847026843}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2234041541080527`, 4.078013847026843}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8156027694053685, 3.262411077621474}]}, {RGBColor[0, 0, 0.7], PointBox[{1.631205538810737, 3.262411077621474}]}, {RGBColor[0, 0, 0.7], PointBox[{0.40780138470268423`, 2.446808308216106}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 1.6312055388107378`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8156027694053685, 1.6312055388107378`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.40780138470268423`, 0.8156027694053698}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8156027694053685, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2234041541080527`, 0.8156027694053698}]}, {RGBColor[0, 0, 0.7], PointBox[{2.85460969291879, 2.446808308216106}]}, {RGBColor[0, 0, 0.7], PointBox[{2.4468083082161054`, 1.6312055388107378`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0390069235134214`, 0.8156027694053698}]}, {RGBColor[0, 0, 0.7], PointBox[{2.85460969291879, 0.8156027694053698}]}, {RGBColor[0, 0, 0.7], PointBox[{3.262411077621474, 1.6312055388107378`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.631205538810737, 4.893616616432212}]}, {RGBColor[0, 0, 0.7], PointBox[{2.0390069235134214`, 5.70921938583758}]}, {RGBColor[0, 0, 0.7], PointBox[{3.262411077621474, 6.524822155242949}]}, {RGBColor[0, 0, 0.7], PointBox[{2.85460969291879, 5.70921938583758}]}, {RGBColor[0, 0, 0.7], PointBox[{3.6702124623241583`, 5.70921938583758}]}, {RGBColor[0, 0, 0.7], PointBox[{2.2429076158647634`, 9.787233232864423}]}, {RGBColor[0, 0, 0.7], PointBox[{1.835106231162079, 8.971630463459054}]}, {RGBColor[0, 0, 0.7], PointBox[{2.650709000567448, 8.971630463459054}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQbVK27M4j/w/2XkX+s22vqTnYf/llLTD5sb2r8dLX y0xUHSDi3+B8mLwDmFZ2CPmw+FeW5Cl7q60BPZUfFR1g5sH4MPWmYHEFuHkw PkT/Lfv4vB+RM2JkHRigIBQsLgWVf2UP40PMY3aAqYfI/0KT/wz1jxhcP8S9 wnD7IPYLwNXD+DD1EJoLbj4q/xbUPGa4eyNQ1L2yR+Xfsk+AijOggRA0cZh7 YOoh/mBzgNkH8z/MfIi7GRzQ1Seg+QPVPb/g4QHTjxpeXA6w8ISZB5OHhDsv nA+JZ0YHWHqIA8v/hcc/JN2wOsD4ADIVHPo= "]]& ], AspectRatio->NCache[Rational[5, 2]^Rational[1, 2], 1.5811388300841898`], FrameTicks->Automatic, ImageSize->{Automatic, 140}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ/V+ofkXSeg4HQYNYD3MpJYcOxbwfZ1JYHUK3hxS8 KVFwKGeZEPHjJzecD1NvXDvDwHm+rMO7rws4+lz44XyY/J7u9oa1IVJw81xm lV0Q5xJ3OLMiVaFp/2f7s2Ba2GEXWN0r+zCw+QIOu8H8X3A+TD3EPC6oOxgc YHyY/DkwzQw3bw/UnB1g+pb9Aag4AxrYhSYOMw+mHuYemHkQf7A7wOw7A6Vh 8ruh7kJXDzPPCBxOvHB+KNSfsPCAyaOGB5cDqv8F4HyYeph7IPEoBOejqv9l fwZqD4wPUw9zDyS+ROF8mDzMPbD0AIvPvJzELXfeCMHje/PniDsT3QXh8lpP M3vUJ4nA+QBQCg8O "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 37}, {6, 7}, {6, 36}, {7, 8}, {7, 25}, {8, 9}, {8, 10}, {10, 11}, {10, 12}, {12, 13}, {12, 20}, {13, 14}, {13, 19}, {14, 15}, {14, 18}, {15, 16}, { 15, 17}, {20, 21}, {20, 22}, {22, 23}, {22, 24}, {25, 26}, {25, 35}, {26, 27}, {26, 28}, {28, 29}, {28, 30}, {30, 31}, {30, 32}, { 32, 33}, {32, 34}, {37, 38}, {37, 39}}]}], { {RGBColor[0, 0, 0.7], PointBox[{3.085637394311902, 9.051203023314914}]}, {RGBColor[0, 0, 0.7], PointBox[{2.674219075070315, 8.22836638483174}]}, {RGBColor[0, 0, 0.7], PointBox[{3.497055713553489, 8.22836638483174}]}, {RGBColor[0, 0, 0.7], PointBox[{3.085637394311902, 7.405529746348566}]}, {RGBColor[0, 0, 0.7], PointBox[{3.908474032795076, 7.405529746348566}]}, {RGBColor[0, 0, 0.7], PointBox[{3.085637394311902, 6.582693107865392}]}, {RGBColor[0, 0, 0.7], PointBox[{2.674219075070315, 5.759856469382218}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2342549577247608`, 4.937019830899044}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8228366384831738, 4.1141831924158705`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6456732769663478`, 4.1141831924158705`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2342549577247608`, 3.291346553932696}]}, {RGBColor[0, 0, 0.7], PointBox[{2.057091596207935, 3.291346553932696}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2342549577247608`, 2.4685099154495225`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8228366384831738, 1.645673276966348}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4114183192415868, 0.8228366384831745}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8228366384831738, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.2342549577247608`, 0.8228366384831745}]}, {RGBColor[0, 0, 0.7], PointBox[{1.6456732769663478`, 1.645673276966348}]}, {RGBColor[0, 0, 0.7], PointBox[{2.879928234691109, 2.4685099154495225`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.4685099154495216`, 1.645673276966348}]}, {RGBColor[0, 0, 0.7], PointBox[{3.2913465539326956`, 1.645673276966348}]}, {RGBColor[0, 0, 0.7], PointBox[{2.879928234691109, 0.8228366384831745}]}, {RGBColor[0, 0, 0.7], PointBox[{3.7027648731742824`, 0.8228366384831745}]}, {RGBColor[0, 0, 0.7], PointBox[{4.11418319241587, 4.937019830899044}]}, {RGBColor[0, 0, 0.7], PointBox[{3.7027648731742824`, 4.1141831924158705`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.2913465539326956`, 3.291346553932696}]}, {RGBColor[0, 0, 0.7], PointBox[{4.11418319241587, 3.291346553932696}]}, {RGBColor[0, 0, 0.7], PointBox[{3.7027648731742824`, 2.4685099154495225`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.525601511657457, 2.4685099154495225`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.11418319241587, 1.645673276966348}]}, {RGBColor[0, 0, 0.7], PointBox[{4.937019830899043, 1.645673276966348}]}, {RGBColor[0, 0, 0.7], PointBox[{4.525601511657457, 0.8228366384831745}]}, {RGBColor[0, 0, 0.7], PointBox[{5.34843815014063, 0.8228366384831745}]}, {RGBColor[0, 0, 0.7], PointBox[{4.525601511657457, 4.1141831924158705`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.497055713553489, 5.759856469382218}]}, {RGBColor[0, 0, 0.7], PointBox[{4.73131067127825, 6.582693107865392}]}, {RGBColor[0, 0, 0.7], PointBox[{4.319892352036663, 5.759856469382218}]}, {RGBColor[0, 0, 0.7], PointBox[{5.142728990519837, 5.759856469382218}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ/V+ofkXSeg4HQYNYD3MpJYcOxbwfZ1JYHUK3hxS8 KVFwKGeZEPHjJzecD1NvXDvDwHm+rMO7rws4+lz44XyY/J7u9oa1IVJw81xm lV0Q5xJ3OLMiVaFp/2f7s2Ba2GEXWN0r+zCw+QIOu8H8X3A+TD3EPC6oOxgc YHyY/DkwzQw3bw/UnB1g+pb9Aag4AxrYhSYOMw+mHuYemHkQf7A7wOw7A6Vh 8ruh7kJXDzPPCBxOvHB+KNSfsPCAyaOGB5cDqv8F4HyYeph7IPEoBOejqv9l fwZqD4wPUw9zDyS+ROF8mDzMPbD0AIvPvJzELXfeCMHje/PniDsT3QXh8lpP M3vUJ4nA+QBQCg8O "]]& ], AspectRatio->NCache[2 3^Rational[-1, 2], 1.1547005383792517`], FrameTicks->Automatic, ImageSize->{Automatic, 110}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ7fX/VK+57h97ruSWtd2RKg5PpHWWu7/6am+46s7m 8yeUHCI+muwStmB0gPFh6sPB4ooOEH0sDjA+TP2fAqnG9X7ycPUeYFrGYUZv 9az93Dftp4FpSQcGKHgMtlfUYTpY/KU9jA9TbwC2Xwjqjk9wPkQ9pwPMPIj7 WR1g+iHu+I+m/qf9L7A4P9Q8JgcYH+JeHgd082Hyf6A0jB/w4//ipZvYHKZA 1c1r27BBdyIzVD+TA0uW/3TZK5xw/pUSqfUxX4Xh6reofd/Xxi0Al992e17X 1K88DhOg7uy7P2+H0xxBOP/LIdv5RvfF4eodA9+t3rVXBC6fMcNt0z8dYSj/ pb0U17SlZX5icP5yk95Jqxik4erPVj+d8S5fEi4PMx8WLzD1MH7DW5OetIky cPWw8IKFNyw9wOJ735XLC5ir2eHpAQBLYRh3 "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 39}, {6, 7}, {6, 38}, {7, 8}, {7, 13}, {8, 9}, {8, 10}, {10, 11}, {10, 12}, {13, 14}, {13, 37}, {14, 15}, {14, 18}, {15, 16}, {15, 17}, {18, 19}, { 18, 20}, {20, 21}, {20, 24}, {21, 22}, {21, 23}, {24, 25}, {24, 28}, {25, 26}, {25, 27}, {28, 29}, {28, 32}, {29, 30}, {29, 31}, { 32, 33}, {32, 36}, {33, 34}, {33, 35}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7610393084323328`, 10.174893782053477`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3696972398918144`, 9.392209644972441}]}, {RGBColor[0, 0, 0.7], PointBox[{2.1523813769728513`, 9.392209644972441}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7610393084323328`, 8.609525507891403}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5437234455133693`, 8.609525507891403}]}, {RGBColor[0, 0, 0.7], PointBox[{2.1523813769728513`, 7.826841370810367}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7610393084323328`, 7.0441572337293294`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.39134206854051845`, 6.261473096648293}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 5.4787889595672565`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.7826841370810368, 5.4787889595672565`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.39134206854051845`, 4.69610482248622}]}, {RGBColor[0, 0, 0.7], PointBox[{1.1740262056215551`, 4.69610482248622}]}, {RGBColor[0, 0, 0.7], PointBox[{3.130736548324147, 6.261473096648293}]}, {RGBColor[0, 0, 0.7], PointBox[{2.7393944797836287`, 5.4787889595672565`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.9567103427025918`, 4.69610482248622}]}, {RGBColor[0, 0, 0.7], PointBox[{1.5653682741620736`, 3.9134206854051827`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.3480524112431103`, 3.9134206854051827`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5220786168646656`, 4.69610482248622}]}, {RGBColor[0, 0, 0.7], PointBox[{3.130736548324147, 3.9134206854051827`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.9134206854051836`, 3.9134206854051827`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.837229996918758, 3.130736548324146}]}, {RGBColor[0, 0, 0.7], PointBox[{2.44588792837824, 2.34805241124311}]}, {RGBColor[0, 0, 0.7], PointBox[{3.228572065459277, 2.34805241124311}]}, {RGBColor[0, 0, 0.7], PointBox[{4.989611373891609, 3.130736548324146}]}, {RGBColor[0, 0, 0.7], PointBox[{4.011256202540313, 2.34805241124311}]}, {RGBColor[0, 0, 0.7], PointBox[{3.619914133999795, 1.565368274162072}]}, {RGBColor[0, 0, 0.7], PointBox[{4.402598271080832, 1.565368274162072}]}, {RGBColor[0, 0, 0.7], PointBox[{5.967966545242906, 2.34805241124311}]}, {RGBColor[0, 0, 0.7], PointBox[{5.185282408161869, 1.565368274162072}]}, {RGBColor[0, 0, 0.7], PointBox[{4.793940339621351, 0.782684137081036}]}, {RGBColor[0, 0, 0.7], PointBox[{5.576624476702387, 0.782684137081036}]}, {RGBColor[0, 0, 0.7], PointBox[{6.7506506823239425`, 1.565368274162072}]}, {RGBColor[0, 0, 0.7], PointBox[{6.359308613783424, 0.782684137081036}]}, {RGBColor[0, 0, 0.7], PointBox[{5.967966545242906, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{6.7506506823239425`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{7.1419927508644605`, 0.782684137081036}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5220786168646656`, 5.4787889595672565`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5437234455133693`, 7.0441572337293294`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.935065514053888, 7.826841370810367}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQ7fX/VK+57h97ruSWtd2RKg5PpHWWu7/6am+46s7m 8yeUHCI+muwStmB0gPFh6sPB4ooOEH0sDjA+TP2fAqnG9X7ycPUeYFrGYUZv 9az93Dftp4FpSQcGKHgMtlfUYTpY/KU9jA9TbwC2Xwjqjk9wPkQ9pwPMPIj7 WR1g+iHu+I+m/qf9L7A4P9Q8JgcYH+JeHgd082Hyf6A0jB/w4//ipZvYHKZA 1c1r27BBdyIzVD+TA0uW/3TZK5xw/pUSqfUxX4Xh6reofd/Xxi0Al992e17X 1K88DhOg7uy7P2+H0xxBOP/LIdv5RvfF4eodA9+t3rVXBC6fMcNt0z8dYSj/ pb0U17SlZX5icP5yk95Jqxik4erPVj+d8S5fEi4PMx8WLzD1MH7DW5OetIky cPWw8IKFNyw9wOJ735XLC5ir2eHpAQBLYRh3 "]]& ], AspectRatio->NCache[Rational[7, 3]^Rational[1, 2], 1.5275252316519468`], FrameTicks->Automatic, ImageSize->{Automatic, 130}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["RandomPathTree", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "RandomPathTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"RandomPathTree[n] gives a pseudorandom path tree with n \ leaves.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571752-4310625"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Table", "[", RowBox[{ RowBox[{"BareTreeForm", "[", RowBox[{"RandomPathTree", "[", "20", "]"}], "]"}], ",", RowBox[{"{", "10", "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq8+/YW37NzK37Z+DAAAWnvlrbt0oaOEDk 39ij8u/Yb38jrSSRqQdXDxHXgatH5d+x//MuOdP4qpZD8if/kJjyr3A+TL3c B3ZeR25NuHqHj6s3+Dmqw9XD+DD1EHFVKP8PnA9T3/b58/fMtcpw9Su+TJ9d /lgRbj7EPwpw9TA+TP0tMC0DNx/Gh6mHuFfSAWIuowOMD1OfAlYnClcPUScI N/8OmOaBuweinhWuHsaHqX8ANRem/gFKOHyF82HqUePlDwYf1bw/cPfA/ANz bzLUHTD/wNTDwhOmHjW8/8DjE+Y+WHoBAA+aPsw= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 39}, {4, 5}, {4, 6}, {6, 7}, {6, 8}, {8, 9}, {8, 38}, {9, 10}, {9, 11}, {11, 12}, {11, 13}, {13, 14}, {13, 37}, {14, 15}, {14, 36}, {15, 16}, {15, 17}, {17, 18}, { 17, 19}, {19, 20}, {19, 21}, {21, 22}, {21, 35}, {22, 23}, {22, 34}, {23, 24}, {23, 33}, {24, 25}, {24, 26}, {26, 27}, {26, 32}, { 27, 28}, {27, 29}, {29, 30}, {29, 31}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 15.20526224699857}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq8+/YW37NzK37Z+DAAAWnvlrbt0oaOEDk 39ij8u/Yb38jrSSRqQdXDxHXgatH5d+x//MuOdP4qpZD8if/kJjyr3A+TL3c B3ZeR25NuHqHj6s3+Dmqw9XD+DD1EHFVKP8PnA9T3/b58/fMtcpw9Su+TJ9d /lgRbj7EPwpw9TA+TP0tMC0DNx/Gh6mHuFfSAWIuowOMD1OfAlYnClcPUScI N/8OmOaBuweinhWuHsaHqX8ANRem/gFKOHyF82HqUePlDwYf1bw/cPfA/ANz bzLUHTD/wNTDwhOmHjW8/8DjE+Y+WHoBAA+aPsw= "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQLfeBndeRm9PB8mtmbt0/A4fkT/4hMeWsDqe+Wtu3 Sho4rPgyfXb5Y0aH7W+klSQy9Rxuvt1/VHX+H3sIrQNXD+PD1P95l5xpfFUL rh5ijyZU/Vd7h4+rN/g5qsPVw/gw9RB1qnD1bZ8/f89cqwyVf2MP0acIVw/j w9RD3K8ANx/Gh6m/BaZl4Ooh7pOEm58CFheFq4fxYeoh5grC1d8B0zxw9TA+ TH0KSji9sX8AVXcDTN+B8t/YM6CBm2jiMPNg6mH2PUAJB0YHmH0wPsy9MD7M v7D4g4UHTB4W3jB51PhgdYDFJyz9wOIbxkdNLzzw9AQAuPQuvw== "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 38}, {3, 4}, {3, 5}, {5, 6}, { 5, 37}, {6, 7}, {6, 36}, {7, 8}, {7, 9}, {9, 10}, {9, 35}, {10, 11}, {10, 34}, {11, 12}, {11, 13}, {13, 14}, {13, 15}, {15, 16}, { 15, 33}, {16, 17}, {16, 32}, {17, 18}, {17, 19}, {19, 20}, {19, 31}, {20, 21}, {20, 22}, {22, 23}, {22, 30}, {23, 24}, {23, 29}, { 24, 25}, {24, 28}, {25, 26}, {25, 27}}]}], { {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.44721359549995787`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 16.099689437998485`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQLfeBndeRm9PB8mtmbt0/A4fkT/4hMeWsDqe+Wtu3 Sho4rPgyfXb5Y0aH7W+klSQy9Rxuvt1/VHX+H3sIrQNXD+PD1P95l5xpfFUL rh5ijyZU/Vd7h4+rN/g5qsPVw/gw9RB1qnD1bZ8/f89cqwyVf2MP0acIVw/j w9RD3K8ANx/Gh6m/BaZl4Ooh7pOEm58CFheFq4fxYeoh5grC1d8B0zxw9TA+ TH0KSji9sX8AVXcDTN+B8t/YM6CBm2jiMPNg6mH2PUAJB0YHmH0wPsy9MD7M v7D4g4UHTB4W3jB51PhgdYDFJyz9wOIbxkdNLzzw9AQAuPQuvw== "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq83kcLL9m5tb9M3CQ+8DO68jN6XDqq7V9 q6SBQ/In/5CYclaH7W+klSQy9Rxg6mF8mHqIuA5c/Z93yZnGV7UcVnyZPrv8 MSNUnabDLbC6P/YOH1dv8HNUh6r/ag+hVeHqYXyY+rbPn79nrlWGq4eoU4TK v7GHuFfB4QaYf8ceIi7jwAAFEPsl4ephfJj6FLC5onDzYXyYeoh9gnD3wPgw 9Xeg4QJTnwINB5j5D6D6YOphfJj6B1AaZj6MD1MP8wcsfGB8mHqYfTB5mHtg +mHhAVMPCy+Yelh4wuIPNbxZHWDxBYtvWHzC0gMsviHmCsDTA4wPS08Anygt Pw== "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 4}, {4, 5}, {4, 38}, {5, 6}, { 5, 37}, {6, 7}, {6, 36}, {7, 8}, {7, 35}, {8, 9}, {8, 10}, {10, 11}, {10, 34}, {11, 12}, {11, 33}, {12, 13}, {12, 32}, {13, 14}, { 13, 31}, {14, 15}, {14, 16}, {16, 17}, {16, 18}, {18, 19}, {18, 20}, {20, 21}, {20, 30}, {21, 22}, {21, 29}, {22, 23}, {22, 24}, { 24, 25}, {24, 26}, {26, 27}, {26, 28}}]}], { {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.788854381999832, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.788854381999832, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0.44721359549995787`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.44721359549995787`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.788854381999832, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.44721359549995787`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{1.788854381999832, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.788854381999832, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.788854381999832, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 16.099689437998485`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq83kcLL9m5tb9M3CQ+8DO68jN6XDqq7V9 q6SBQ/In/5CYclaH7W+klSQy9Rxg6mF8mHqIuA5c/Z93yZnGV7UcVnyZPrv8 MSNUnabDLbC6P/YOH1dv8HNUh6r/ag+hVeHqYXyY+rbPn79nrlWGq4eoU4TK v7GHuFfB4QaYf8ceIi7jwAAFEPsl4ephfJj6FLC5onDzYXyYeoh9gnD3wPgw 9Xeg4QJTnwINB5j5D6D6YOphfJj6B1AaZj6MD1MP8wcsfGB8mHqYfTB5mHtg +mHhAVMPCy+Yelh4wuIPNbxZHWDxBYtvWHzC0gMsviHmCsDTA4wPS08Anygt Pw== "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQveLL9NnljxkdLL9m5tb9M3C4+Xb/UdX5f+xPfbW2 b5U0cEj+5B8SU/7VfvsbaSWJTD0HmHoYH6YeQuvA1f95l5xpfFULrh7Gh6mX +8DO68itCVXP6gDjw9Q7fFy9wc9RHSrOCefD1ENoVbj6ts+fv2euVYabDxFX hKuH8WHqIf5TgKu/BaZl4O6H2CvpABF/Y58CFheFq4fxYeoh5grC1d8B0zxQ /h2oela4ehgfpv4BijvuQPlv7BnQwC00cZh5MPUw9z1AiZc/cPfA/A9zL4wP 828yirtk4OEPCy8YHxbet6DmwuIDph81PbA6wNITACXiLcg= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 4}, {4, 5}, {4, 38}, {5, 6}, { 5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 37}, {12, 13}, {12, 36}, {13, 14}, {13, 15}, {15, 16}, {15, 35}, {16, 17}, { 16, 34}, {17, 18}, {17, 33}, {18, 19}, {18, 20}, {20, 21}, {20, 32}, {21, 22}, {21, 31}, {22, 23}, {22, 24}, {24, 25}, {24, 30}, { 25, 26}, {25, 29}, {26, 27}, {26, 28}}]}], { {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.447213595499958, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.447213595499958, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{3.577708763999664, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 16.099689437998485`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQveLL9NnljxkdLL9m5tb9M3C4+Xb/UdX5f+xPfbW2 b5U0cEj+5B8SU/7VfvsbaSWJTD0HmHoYH6YeQuvA1f95l5xpfFULrh7Gh6mX +8DO68itCVXP6gDjw9Q7fFy9wc9RHSrOCefD1ENoVbj6ts+fv2euVYabDxFX hKuH8WHqIf5TgKu/BaZl4O6H2CvpABF/Y58CFheFq4fxYeoh5grC1d8B0zxQ /h2oela4ehgfpv4BijvuQPlv7BnQwC00cZh5MPUw9z1AiZc/cPfA/A9zL4wP 828yirtk4OEPCy8YHxbet6DmwuIDph81PbA6wNITACXiLcg= "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq83kcLL9m5tb9M3CQ+8DO68jN6XDqq7V9 q6SBQ/In/5CYclaH7W+klSQy9RxWfJk+u/wxowNEnw6U/mP/511ypvFVLaj6 r/YQczSh8m/sHT6u3uDnqA7l37GHqFOFq4fxYerbPn/+nrlWGa4eYq+iAwMU QNynAFePyr9jfwtMy8DNh/Fh6iHuk4SrTwGrE4Wrh/Fh6iH2C8L9C+PD1N+B hiMsfGB8mPoUaDjC1D9AMYfRAcaHqX8AtRcW/g9Q3MEIDwdYfMH4MPUw+2Dm wfwLsx8WnjB51PD+A48vmH2w+ISZD4tvmP2o6YEHnl4g8SIAT08ACHEwKA== "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 38}, {3, 4}, {3, 37}, {4, 5}, { 4, 36}, {5, 6}, {5, 35}, {6, 7}, {6, 34}, {7, 8}, {7, 9}, {9, 10}, { 9, 33}, {10, 11}, {10, 32}, {11, 12}, {11, 13}, {13, 14}, {13, 15}, {15, 16}, {15, 31}, {16, 17}, {16, 18}, {18, 19}, {18, 20}, { 20, 21}, {20, 22}, {22, 23}, {22, 30}, {23, 24}, {23, 25}, {25, 26}, {25, 27}, {27, 28}, {27, 29}}]}], { {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 16.099689437998485`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq83kcLL9m5tb9M3CQ+8DO68jN6XDqq7V9 q6SBQ/In/5CYclaH7W+klSQy9RxWfJk+u/wxowNEnw6U/mP/511ypvFVLaj6 r/YQczSh8m/sHT6u3uDnqA7l37GHqFOFq4fxYerbPn/+nrlWGa4eYq+iAwMU QNynAFePyr9jfwtMy8DNh/Fh6iHuk4SrTwGrE4Wrh/Fh6iH2C8L9C+PD1N+B hiMsfGB8mPoUaDjC1D9AMYfRAcaHqX8AtRcW/g9Q3MEIDwdYfMH4MPUw+2Dm wfwLsx8WnjB51PD+A48vmH2w+ISZD4tvmP2o6YEHnl4g8SIAT08ACHEwKA== "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq8//YW37NzK37Z+CQ/Mk/JKb8q/2pr9b2 rZIGDiu+TJ9d/pjRAcaHqd/+RlpJIlMPrh4iruNwC0y/sf/zLjnT+KoWlH/H Xu4DO68jt6YDAxQ4fFy9wc9RHa4elX/HHmKuKtx8GB+mvu3z5++Za5Xh7oHx Yeoh7laEux/Gh6mH+EcBqp7VAcaHqYfYI+MAcTcnnA9TDxGXhIrzwPkw9Slg daJQcwXgfJh6iD2CcPV3oOIw9TA+TH0K1F6YvhQUdws4PID6qxUcDsJwPkz9 A2i4JUPdAePD1MPixREcD+JwPkw/jIaFLyw+YeEJi29Y+MHSAyy8YOkFAOKt KZ8= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 39}, {4, 5}, {4, 38}, {5, 6}, { 5, 37}, {6, 7}, {6, 36}, {7, 8}, {7, 9}, {9, 10}, {9, 11}, {11, 12}, {11, 13}, {13, 14}, {13, 15}, {15, 16}, {15, 17}, {17, 18}, { 17, 19}, {19, 20}, {19, 21}, {21, 22}, {21, 23}, {23, 24}, {23, 35}, {24, 25}, {24, 26}, {26, 27}, {26, 28}, {28, 29}, {28, 30}, { 30, 31}, {30, 32}, {32, 33}, {32, 34}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.447213595499958, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.447213595499958, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{0.894427190999916, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{3.577708763999664, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{3.577708763999664, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.577708763999664, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{4.47213595499958, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{4.024922359499621, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.919349550499537, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{4.47213595499958, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{5.366563145999495, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{4.919349550499537, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{5.813776741499454, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{4.47213595499958, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 15.20526224699857}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq8//YW37NzK37Z+CQ/Mk/JKb8q/2pr9b2 rZIGDiu+TJ9d/pjRAcaHqd/+RlpJIlMPrh4iruNwC0y/sf/zLjnT+KoWlH/H Xu4DO68jt6YDAxQ4fFy9wc9RHa4elX/HHmKuKtx8GB+mvu3z5++Za5Xh7oHx Yeoh7laEux/Gh6mH+EcBqp7VAcaHqYfYI+MAcTcnnA9TDxGXhIrzwPkw9Slg daJQcwXgfJh6iD2CcPV3oOIw9TA+TH0K1F6YvhQUdws4PID6qxUcDsJwPkz9 A2i4JUPdAePD1MPixREcD+JwPkw/jIaFLyw+YeEJi29Y+MHSAyy8YOkFAOKt KZ8= "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQnfzJPySm/Ku95dfM3Lp/Bg433+4/qjr/jf2pr9b2 rZIw/h84H6Z++xtpJYlMPYcVX6bPLn/M6ADjw9RDaB2oelYHGB+m/s+75Ezj q1oOch/YeR25OeF8mHqIuCZcvcPH1Rv8HNXh5kPUqcLd0/b58/fMtcpw90P0 KcLVw/gw9RD/KMDV3wLTMnD1MD5MPcQ9knD1KWBxUSj/DtR8QQcGKLgDFueB q0fl34HqZ4Wbn4ISTm/sH6CE4x0o/409Axq4iSYOMw+mHuafByjh9hXuXpg8 zD+w8Ib5F8aHhReMDwvvZBR/qMLjEzW+eODxCQA7ZjGR "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 3}, {3, 4}, {3, 5}, {5, 6}, {5, 7}, {7, 8}, {7, 9}, {9, 10}, {9, 39}, {10, 11}, {10, 38}, {11, 12}, {11, 37}, {12, 13}, {12, 36}, {13, 14}, {13, 15}, {15, 16}, {15, 35}, {16, 17}, { 16, 18}, {18, 19}, {18, 34}, {19, 20}, {19, 33}, {20, 21}, {20, 32}, {21, 22}, {21, 23}, {23, 24}, {23, 25}, {25, 26}, {25, 31}, { 26, 27}, {26, 30}, {27, 28}, {27, 29}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 12.521980673998822`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQnfzJPySm/Ku95dfM3Lp/Bg433+4/qjr/jf2pr9b2 rZIw/h84H6Z++xtpJYlMPYcVX6bPLn/M6ADjw9RDaB2oelYHGB+m/s+75Ezj q1oOch/YeR25OeF8mHqIuCZcvcPH1Rv8HNXh5kPUqcLd0/b58/fMtcpw90P0 KcLVw/gw9RD/KMDV3wLTMnD1MD5MPcQ9knD1KWBxUSj/DtR8QQcGKLgDFueB q0fl34HqZ4Wbn4ISTm/sH6CE4x0o/409Axq4iSYOMw+mHuafByjh9hXuXpg8 zD+w8Ib5F8aHhReMDwvvZBR/qMLjEzW+eODxCQA7ZjGR "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQLfeBndeRm9PB8mtmbt0/A4fkT/4hMeWsDqe+Wtu3 Sho4rPgyfXb5Y0aH7W+klSQy9Rxuvt1/VHX+H3sIrQNXD+PD1P95l5xpfFUL rh5ijyZU/Vd7h4+rN/g5qkPl39hDxFXh6mF8mPq2z5+/Z65VhquH2KPocAPM v2MPca8CXD2MD1N/C0zLwNVD3CPpwAAFKWB9onD1MD5MPcQ+Qbj5MD5M/R0w zQN3P4wPU58CDSdY+KSghNsf+wco/v4K5cP8yegA48PUw9wNC390Prp5MP/C 9MPCA8aHhSfMPlh4w/iw+IKZD4tPWPqBxTeMj5peeODpCQDF+jA9 "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 38}, {3, 4}, {3, 5}, {5, 6}, { 5, 37}, {6, 7}, {6, 36}, {7, 8}, {7, 35}, {8, 9}, {8, 10}, {10, 11}, {10, 34}, {11, 12}, {11, 33}, {12, 13}, {12, 14}, {14, 15}, { 14, 32}, {15, 16}, {15, 31}, {16, 17}, {16, 18}, {18, 19}, {18, 20}, {20, 21}, {20, 22}, {22, 23}, {22, 24}, {24, 25}, {24, 30}, { 25, 26}, {25, 27}, {27, 28}, {27, 29}}]}], { {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.44721359549995787`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{0.44721359549995787`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{0.44721359549995787`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{3.5777087639996634`, 16.099689437998485`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQLfeBndeRm9PB8mtmbt0/A4fkT/4hMeWsDqe+Wtu3 Sho4rPgyfXb5Y0aH7W+klSQy9Rxuvt1/VHX+H3sIrQNXD+PD1P95l5xpfFUL rh5ijyZU/Vd7h4+rN/g5qkPl39hDxFXh6mF8mPq2z5+/Z65VhquH2KPocAPM v2MPca8CXD2MD1N/C0zLwNVD3CPpwAAFKWB9onD1MD5MPcQ+Qbj5MD5M/R0w zQN3P4wPU58CDSdY+KSghNsf+wco/v4K5cP8yegA48PUw9wNC390Prp5MP/C 9MPCA8aHhSfMPlh4w/iw+IKZD4tPWPqBxTeMj5peeODpCQDF+jA9 "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq89/YW37NzK37Z+AA4d+xP/XV2r5V0sCB AQq2v5FWksjUc4CpR+XfsYfQOg7Jn/xDYsq/wvkw9X/eJWcaX9WCq5f7wM7r yK0JVw/jw9Q7fFy9wc9RHa4eok4V7p62z5+/Z65VhqtH5d+xX/Fl+uzyx4pw 82F8mHqI/xTg6m+BaRm4ehgfph7iPkko/w+cD1OfAqZFHSD2MDrA+DD1EHFB qHpWBxgfpv4OWB0PXH0KVB1MfQqKPkaHB1B1MPUPoO6EqYfxYeph4QZxNycG /wGKvzgx3AMLL5h/YfEBk0eNrz/w+Iaph6UnADTUMZg= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 4}, {4, 5}, {4, 6}, {6, 7}, {6, 38}, {7, 8}, {7, 9}, {9, 10}, {9, 37}, {10, 11}, {10, 36}, {11, 12}, {11, 13}, {13, 14}, {13, 15}, {15, 16}, {15, 35}, {16, 17}, { 16, 18}, {18, 19}, {18, 20}, {20, 21}, {20, 22}, {22, 23}, {22, 24}, {24, 25}, {24, 34}, {25, 26}, {25, 27}, {27, 28}, {27, 33}, { 28, 29}, {28, 30}, {30, 31}, {30, 32}}]}], { {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{3.1304951684997055`, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 16.099689437998485`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQffPt/qOq89/YW37NzK37Z+AA4d+xP/XV2r5V0sCB AQq2v5FWksjUc4CpR+XfsYfQOg7Jn/xDYsq/wvkw9X/eJWcaX9WCq5f7wM7r yK0JVw/jw9Q7fFy9wc9RHa4eok4V7p62z5+/Z65VhqtH5d+xX/Fl+uzyx4pw 82F8mHqI/xTg6m+BaRm4ehgfph7iPkko/w+cD1OfAqZFHSD2MDrA+DD1EHFB qHpWBxgfpv4OWB0PXH0KVB1MfQqKPkaHB1B1MPUPoO6EqYfxYeph4QZxNycG /wGKvzgx3AMLL5h/YfEBk0eNrz/w+Iaph6UnADTUMZg= "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]], ",", GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxTTMoPSmViYGBQB2IQnfzJPySm/Ku95dfM3Lp/Bg433+4/qjr/jf2pr9b2 rZIw/h377W+klSQy9Rxg6mF8mHoIrQNX/+ddcqbxVS0HBiiQ+8DO68itCVeP yr9j7/Bx9QY/R3W4+TA+TD1EXBXK/wPnw9S3ff78PXOtMlz9ii/TZ5c/VoSr h/Fh6iH+U4CrvwWmZeDugbhPEq4exoepTwGLi8LVQ8wXhKuH8WHq74BpHrh7 YHyYeoh5rHD1D6DqYOofoPj7K5QP8yejwwOUePhjDwv3ZKi5MD5MPap9f9D8 8wceHjD1sPCC8WHhDXMPLL5vorhbB86HpScAFJZCKw== "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 39}, {2, 3}, {2, 4}, {4, 5}, {4, 38}, {5, 6}, { 5, 37}, {6, 7}, {6, 8}, {8, 9}, {8, 10}, {10, 11}, {10, 12}, {12, 13}, {12, 36}, {13, 14}, {13, 15}, {15, 16}, {15, 35}, {16, 17}, { 16, 34}, {17, 18}, {17, 19}, {19, 20}, {19, 33}, {20, 21}, {20, 22}, {22, 23}, {22, 24}, {24, 25}, {24, 32}, {25, 26}, {25, 27}, { 27, 28}, {27, 29}, {29, 30}, {29, 31}}]}], { {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 16.994116628998402`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 16.099689437998485`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 15.20526224699857}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{0., 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 12.521980673998822`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 11.627553482998906`}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 10.73312629199899}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 8.94427190999916}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 6.260990336999411}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{0.4472135954999579, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 4.47213595499958}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 3.5777087639996648`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{0.8944271909999159, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 1.7888543819998333`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 0.8944271909999166}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.6832815729997477`, 0.}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 2.683281572999748}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 5.366563145999496}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 7.155417527999328}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 8.049844718999243}]}, {RGBColor[0, 0, 0.7], PointBox[{2.23606797749979, 9.838699100999076}]}, {RGBColor[0, 0, 0.7], PointBox[{1.3416407864998738`, 13.416407864998739`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 14.310835055998654`}]}, {RGBColor[0, 0, 0.7], PointBox[{1.7888543819998317`, 16.099689437998485`}]}}}, ContentSelectable->True], Annotation[#, VertexCoordinateRules -> CompressedData[" 1:eJxTTMoPSmViYGBQB2IQnfzJPySm/Ku95dfM3Lp/Bg433+4/qjr/jf2pr9b2 rZIw/h377W+klSQy9Rxg6mF8mHoIrQNX/+ddcqbxVS0HBiiQ+8DO68itCVeP yr9j7/Bx9QY/R3W4+TA+TD1EXBXK/wPnw9S3ff78PXOtMlz9ii/TZ5c/VoSr h/Fh6iH+U4CrvwWmZeDugbhPEq4exoepTwGLi8LVQ8wXhKuH8WHq74BpHrh7 YHyYeoh5rHD1D6DqYOofoPj7K5QP8yejwwOUePhjDwv3ZKi5MD5MPap9f9D8 8wceHjD1sPCC8WHhDXMPLL5vorhbB86HpScAFJZCKw== "]]& ], AspectRatio->NCache[2 Rational[5, 3]^Rational[1, 2], 2.581988897471611], FrameTicks->Automatic, ImageSize->{Automatic, 190}, PlotRange->All, PlotRangePadding->Scaled[0.1]]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["RankBinaryTree", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "RankBinaryTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"RankBinaryTree[tree] gives the rank of an n\[Hyphen]leaf \ binary tree in BinaryTrees[n].\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571756-9267165"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"RankBinaryTree", "[", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}]}], "}"}], "]"}]], "Input"], Cell[BoxData["109"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"BinaryTrees", "[", "9", "]"}], "\[LeftDoubleBracket]", "109", "\[RightDoubleBracket]"}], "\[Equal]", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", "}"}]}], "}"}]}], "}"}]}], "}"}]}]], "Input"], Cell[BoxData["True"], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["RankTree", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "RankTree"}]], "Input"], Cell[BoxData[ StyleBox["\<\"RankTree[tree] gives the rank of an n\[Hyphen]vertex tree in \ Trees[n].\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571760-9267165"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"RankTree", "[", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"{", "}"}], "}"}]}], "}"}]}], "}"}], "}"}], "]"}]], "Input"], Cell[BoxData["275"], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"Trees", "[", "9", "]"}], "\[LeftDoubleBracket]", "275", "\[RightDoubleBracket]"}], "\[Equal]", RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", "}"}], ",", RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"{", "}"}], "}"}]}], "}"}]}], "}"}], "}"}]}]], "Input"], Cell[BoxData["True"], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["TreeChop", "Input"]], "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"?", "TreeChop"}]], "Input"], Cell[BoxData[ StyleBox["\<\"TreeChop[expr, d] replaces all subexpressions of expr at depth \ d with {}.\"\>", "MSG"]], "Print", "PrintUsage", CellTags->"Info3502571763-9267165"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"tree", "=", RowBox[{"CompleteBinaryTree", "[", "64", "]"}]}], ";"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"BareTreeForm", "[", "tree", "]"}]], "Input"], Cell[BoxData[ GraphicsBox[ TagBox[GraphicsGroupBox[{GraphicsComplexBox[CompressedData[" 1:eJxdlE1OAkEQhUejRo0aRERERIZ/hr/5cz19BuN4ABPXHkHOo+fwCLN348YV MSExJCYKNXSnv0pI87req3pVM+A+Pt89bTuO8/L/WZ0SHZV/UW+vqyjl5zKR 6x31kK5ikcj9d34/z8+PRPKfyfpI35P79ZklDiLFvdT70vw0r2Or5omt/9X9 5PYH+gXqL6HfUvCnbP428Ina+BD9gdr0l/yesvvvar3EPvCR5ov+UOdFfwx+ Ef0K8F+A/hT4DP2KqF8C/0Y/b7mtYv4LZe+/jPnPsb8ycAX+K+h/CX5N2e/X Feapar5EDbgOf9eoX0f/pp5XThf9G/DfQD1iF/1d+GuC38J+W5jX8KVeC7gN f23UJ57q37voPfzee3ofku/ifexgPv1/kkcXuId5TF70PfAH2H8f8/UxD/EA /gao7wGP9byiH+J5DOHf6KX+EHgEvyP4G4E/wX7H8D/WfIkJ8BT+TF70U5s/ C+3n7QV6fsn7th/Pxzw+6gNnPvyYvEQAfmDvexZgfsOXesBeCH8h/AFnkZ5X 9JH9vmUh/Bu9RGTjWQS/Ji968mPsN4b/GP6Bsxj+Yru+c6vxH21O7Kw= "], {RGBColor[0.55, 0.45, 0.45], LineBox[{{1, 2}, {1, 65}, {2, 3}, {2, 34}, {3, 4}, {3, 19}, {4, 5}, {4, 12}, {5, 6}, {5, 9}, {6, 7}, {6, 8}, {9, 10}, {9, 11}, {12, 13}, {12, 16}, {13, 14}, {13, 15}, {16, 17}, {16, 18}, {19, 20}, {19, 27}, {20, 21}, {20, 24}, {21, 22}, {21, 23}, {24, 25}, {24, 26}, {27, 28}, {27, 31}, {28, 29}, {28, 30}, {31, 32}, {31, 33}, {34, 35}, {34, 50}, {35, 36}, {35, 43}, {36, 37}, {36, 40}, {37, 38}, {37, 39}, {40, 41}, {40, 42}, {43, 44}, {43, 47}, {44, 45}, {44, 46}, {47, 48}, {47, 49}, {50, 51}, {50, 58}, {51, 52}, {51, 55}, {52, 53}, {52, 54}, {55, 56}, {55, 57}, {58, 59}, {58, 62}, {59, 60}, {59, 61}, {62, 63}, {62, 64}, {65, 66}, {65, 97}, {66, 67}, {66, 82}, {67, 68}, {67, 75}, {68, 69}, {68, 72}, {69, 70}, {69, 71}, {72, 73}, {72, 74}, {75, 76}, {75, 79}, {76, 77}, {76, 78}, {79, 80}, {79, 81}, {82, 83}, {82, 90}, {83, 84}, {83, 87}, {84, 85}, {84, 86}, {87, 88}, {87, 89}, {90, 91}, {90, 94}, {91, 92}, {91, 93}, {94, 95}, {94, 96}, {97, 98}, {97, 113}, {98, 99}, { 98, 106}, {99, 100}, {99, 103}, {100, 101}, {100, 102}, {103, 104}, { 103, 105}, {106, 107}, {106, 110}, {107, 108}, {107, 109}, {110, 111}, {110, 112}, {113, 114}, {113, 121}, {114, 115}, {114, 118}, { 115, 116}, {115, 117}, {118, 119}, {118, 120}, {121, 122}, {121, 125}, {122, 123}, {122, 124}, {125, 126}, {125, 127}}]}], { {RGBColor[0, 0, 0.7], PointBox[{10.5, 2.}]}, {RGBColor[0, 0, 0.7], PointBox[{5.166666666666667, 1.6666666666666667`}]}, {RGBColor[0, 0, 0.7], PointBox[{2.5, 1.3333333