%
% komposition.tex -- Komposition zweier Permutationen
%
% (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}
\usetikzlibrary{decorations.pathreplacing}
\begin{document}
\def\skala{1}
\begin{tikzpicture}[>=latex,thick,scale=\skala]

\begin{scope}[xshift=-4.0cm]

\def\s{0.527}
\def\o{0.133}

\def\verbindung#1{
\fill[color=red!20] ({\o+(#1*\s)},-1.0) rectangle ({\o+(#1*\s)+0.3},0.0);
}

\verbindung{1}
\verbindung{2}
\verbindung{3}
\verbindung{4}
\verbindung{5}
\verbindung{6}


\node at (0,0) {$\displaystyle
\sigma_1=\begin{pmatrix}
1&2&3&4&5&6\\
2&1&3&5&6&4
\end{pmatrix}
%$};
=\begin{pmatrix}
1&2&3&4&5&6\\
2&1&3&5&6&4
\end{pmatrix}$};
\node at (0,-1) {$\displaystyle
\sigma_2=\begin{pmatrix}
1&2&3&4&5&6\\
3&4&5&6&1&2
\end{pmatrix}
=
\begin{pmatrix}
2&1&3&5&6&4\\
4&3&5&1&2&6
\end{pmatrix}
$};
\end{scope}

%\begin{scope}
%\node at (0,0) {$\displaystyle
%\begin{pmatrix}
%1&2&3&4&5&6\\
%2&1&3&5&6&4
%\end{pmatrix}$};
%\node at (0,-1) {$\displaystyle
%\begin{pmatrix}
%2&1&3&5&6&4\\
%4&3&5&1&2&6
%\end{pmatrix}
%$};
%\end{scope}

\draw[decorate,decoration={brace,amplitude=4pt}]
(0,0.4) -- (0,-1.4);

\begin{scope}[xshift=3.1cm]
\node at (0,-0.5) {$\displaystyle
\Rightarrow\quad
\sigma_2\sigma_1=\begin{pmatrix}
1&2&3&4&5&6\\
4&3&5&1&2&6
\end{pmatrix}
$};
\end{scope}

\end{tikzpicture}
\end{document}