%
% zyklenzerlegung.tex -- Zerlegung einer Permutation in Zyklen
%
% (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}
\definecolor{darkgreen}{rgb}{0,0.6,0}
\def\skala{1}
\begin{tikzpicture}[>=latex,thick,scale=\skala]

\begin{scope}[xshift=-3cm]
\node at (0,0) {$\displaystyle
\sigma=\begin{pmatrix}
{\color{red}1}&{\color{red}2}&{\color{darkgreen}3}&{\color{blue}4}&{\color{blue}5}&{\color{blue}6}\\
{\color{red}2}&{\color{red}1}&{\color{darkgreen}3}&{\color{blue}5}&{\color{blue}6}&{\color{blue}4}
\end{pmatrix}$};
\end{scope}
\node at (0,0) {$\mathstrut=\mathstrut$};
\begin{scope}[xshift=1.5cm]
\coordinate (A) at (0,0.5);
\coordinate (B) at (0,-0.5);
\draw[->,color=red] (A) to[out=-20,in=20] (0,-0.5);
\draw[->,color=red] (B) to[out=160,in=-160] (0,0.5);
\node at (A) [above] {$\tiny 1$};
\node at (B) [below] {$\tiny 2$};
\fill (A) circle[radius=0.05];
\fill (B) circle[radius=0.05];

\coordinate (C) at (1.5,0.25);
\node at (C) [above] {$\tiny 3$};
\draw[->,color=darkgreen] ({1.5+0.01},0.25) to[out=-10,in=-170] ({1.5-0.01},0.25);
\draw[color=darkgreen] (1.5,{0.25-0.3}) circle[radius=0.3];
\fill (C) circle[radius=0.05];

\def\r{0.5}
\coordinate (D) at ({3.5+\r*cos(90)},{0+\r*sin(90)});
\coordinate (E) at ({3.5+\r*cos(210)},{0+\r*sin(210)});
\coordinate (F) at ({3.5+\r*cos(330)},{0+\r*sin(330)});
\node at (D) [above] {$\tiny 4$};
\node at (E) [below left] {$\tiny 5$};
\node at (F) [below right] {$\tiny 6$};
\draw[->,color=blue] (D) to[out=180,in=120] (E);
\draw[->,color=blue] (E) to[out=-60,in=-120] (F);
\draw[->,color=blue] (F) to[out=60,in=0] (D);
\fill (D) circle[radius=0.05];
\fill (E) circle[radius=0.05];
\fill (F) circle[radius=0.05];

\end{scope}

\end{tikzpicture}
\end{document}