Merge pull request #1 from AndreasFMueller/master

update

1 files changed, 103 insertions, 0 deletions

diff --git a/buch/chapters/50-permutationen/images/transpositionen.tex b/buch/chapters/50-permutationen/images/transpositionen.tex
new file mode 100644
index 0000000..0670a2c
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+++ b/buch/chapters/50-permutationen/images/transpositionen.tex
@@ -0,0 +1,103 @@
+%
+% transpositionen.tex -- Darstellung eines Zyklus aus Transpositionen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{amsmath}
+\usepackage{times}
+\usepackage{txfonts}
+\usepackage{pgfplots}
+\usepackage{csvsimple}
+\usetikzlibrary{arrows,intersections,math}
+\begin{document}
+\def\skala{1}
+
+\def\kreuz#1#2#3{
+	\draw[->] ({(#1)-1},#2) to[out=-90,in=90] ({#1},{#2-1});
+	\draw[->] ({#1},#2) to[out=-90,in=90] ({#1-1},{#2-1});
+	\node at ({(#1)-0.5+0.2},{#2-0.5}) [right] {$#3$};
+}
+\begin{tikzpicture}[>=latex,thick,scale=\skala]
+\foreach \x in {1,2,3,6,7,8,9}{
+	\fill ({\x-1},0) circle[radius=0.05];
+}
+\foreach \x in {1,2,3}{
+	\node at ({\x-1},0) [above] {$\tiny \x$};
+}
+\node at (8,0) [above] {$\tiny k$};
+\node at (7,0) [above] {$\tiny k-1$};
+\node at (6,0) [above] {$\tiny k-2$};
+\node at (5,0) [above] {$\tiny k-3$};
+\foreach \x in {1,2,3,4,7,8,9}{
+	\fill ({\x-1},-8) circle[radius=0.05];
+}
+\foreach \x in {1,2,3,4}{
+	\node at ({\x-1},-8) [below] {$\tiny \x$};
+}
+\node at (6,-8) [below] {$k-2$};
+\node at (7,-8) [below] {$k-1$};
+\node at (8,-8) [below] {$k$};
+
+\foreach \x in {3,3.2,...,5}{
+	\fill (\x,{-8+\x}) circle[radius=0.02];
+	\fill ({\x+0.5},-8) circle[radius=0.02];
+	\fill ({\x-0.5},0) circle[radius=0.02];
+}
+
+\kreuz{8}{0}{\tau_{k-1,k}}
+\kreuz{7}{-1}{\tau_{k-2,k-1}}
+\kreuz{6}{-2}{\tau_{k-3,k-2}}
+%\kreuz{5}{-3}{\tau_{56}}
+%\kreuz{4}{-4}{\tau_{45}}
+\kreuz{3}{-5}{\tau_{34}}
+\kreuz{2}{-6}{\tau_{23}}
+\kreuz{1}{-7}{\tau_{12}}
+
+\draw[->,color=gray] (0,0) -- (0,-7);
+\draw[->,color=gray] (1,0) -- (1,-6);
+\draw[->,color=gray] (2,0) -- (2,-5);
+%\draw[->,color=gray] (3,0) -- (3,-4);
+%\draw[->,color=gray] (4,0) -- (4,-3);
+\draw[->,color=gray] (5,0) -- (5,-2);
+\draw[->,color=gray] (6,0) -- (6,-1);
+
+\draw[->,color=gray] (8,-1) -- (8,-8);
+\draw[->,color=gray] (7,-2) -- (7,-8);
+\draw[->,color=gray] (6,-3) -- (6,-8);
+%\draw[->,color=gray] (5,-4) -- (5,-8);
+%\draw[->,color=gray] (4,-5) -- (4,-8);
+\draw[->,color=gray] (3,-6) -- (3,-8);
+\draw[->,color=gray] (2,-7) -- (2,-8);
+	
+\fill (6,-1) circle[radius=0.05];
+\fill (7,-1) circle[radius=0.05];
+\fill (8,-1) circle[radius=0.05];
+
+\fill (5,-2) circle[radius=0.05];
+\fill (6,-2) circle[radius=0.05];
+\fill (7,-2) circle[radius=0.05];
+
+%\fill (4,-3) circle[radius=0.05];
+\fill (5,-3) circle[radius=0.05];
+\fill (6,-3) circle[radius=0.05];
+
+%\fill (3,-4) circle[radius=0.05];
+%\fill (4,-4) circle[radius=0.05];
+%\fill (5,-4) circle[radius=0.05];
+
+\fill (2,-5) circle[radius=0.05];
+\fill (3,-5) circle[radius=0.05];
+%\fill (4,-5) circle[radius=0.05];
+
+\fill (1,-6) circle[radius=0.05];
+\fill (2,-6) circle[radius=0.05];
+\fill (3,-6) circle[radius=0.05];
+
+\fill (0,-7) circle[radius=0.05];
+\fill (1,-7) circle[radius=0.05];
+\fill (2,-7) circle[radius=0.05];
+
+\end{tikzpicture}
+\end{document}
+