# Illustrating permutations as braided group - TiKZ-PGF

I would like to illustrate the permutation group using the braid package in TikZ-PGF, such as this image (from Wikipedia):

In fact I would like to illustrate the permutation group for N = 3, which should have 6 total configurations. Having followed the example provided, I so far have:

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\usepackage{braids}

\begin{document}

\begin{tikzpicture}
\braid[style strands={1}{red},style
strands={2}{blue},style strands={3}{green}]  (TEST2) at (5,0) s_1
s_3^{-1} s_1 s_2^{−1} s_1 s_2^{−1};
\end{tikzpicture}
\end{document}


However, I am finding it difficult to understand how to change the ordering. Any help would be appreciated.

My apologies for being a bit late to the party, but here's the permutations of 3 objects represented as braids using the braids package.

\documentclass[tikz,border=1cm]{standalone}
%\url{https://tex.stackexchange.com/q/455488/86}
\usepackage{tikz}
\usepackage{braids}

\begin{document}

\begin{tikzpicture}[
/pgf/braid/.cd,
style strands={1}{red},
style strands={2}{blue},
style strands={3}{green},
number of strands=3
]
\braid (identity) at (0,0) 1 1 1;
\node at ([yshift=-1cm]identity-rev-2-e) {Identity};

\braid (123) at ([xshift=2cm]identity-3-s) 1 s_2^{-1} s_1;
\node at ([yshift=-1cm]123-rev-2-e) {$$(123)$$};

\braid (321) at ([xshift=2cm]123-3-s) 1 s_1^{-1} s_2;
\node at ([yshift=-1cm]321-rev-2-e) {$$(321)$$};

\braid (12) at ([yshift=-2cm]identity-rev-1-e) 1 s_1^{-1} 1;
\node at ([yshift=-1cm]12-rev-2-e) {$$(12)$$};

\braid (23) at ([yshift=-2cm]123-rev-1-e) 1 s_2 1;
\node at ([yshift=-1cm]23-rev-2-e) {$$(23)$$};

\braid (31) at ([yshift=-2cm]321-rev-1-e) s_1^{-1} s_2 s_1^{-1};
\node at ([yshift=-1cm]31-rev-2-e) {$$(31)$$};

\end{tikzpicture}
\end{document}


Obviously, I had free choice on the over-under crossings.

Result:

• I should note that this uses the more recent version of the braids package which isn't as yet available on CTAN (but is on github). – Loop Space Mar 9 at 10:27
• Better late than never ;) Is there some user manual? I don't get the syntax for this but it's exactly what I wanted. – Sid Mar 14 at 3:06