Brackets in a Permutation

Question

I'm having a really hard time doing what I thought would be simple.

I have this permutation:

\pi=\left(\begin{array}{cccccccccccc}
1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
2 & 1 & 3 & 4 & 5 & 9 & 6 & 7 & 8  \\
\end{array}\right)

and I want the sequence 345 to have a brace labelled $\sigma$ and I need the sequence 678 to have the same thing.

@DaiBowen Hello, yes I have already tried it. It doesn't work because my numbers in the bottom row are no longer aligned with the ones on the first row. — hugh_maths, Jun 30 '23 at 15:08

score 2 · Accepted Answer · answered Jun 30 '23 at 15:16

You can use nicematrix, but

the space occupied by the overbraces is not taken into account;
we need a trick to move the parenthesis a bit farther from the matrix.

In order to fix point 1, a phantom tall enough is added. For 2, some explicit spacing. I guess you wanted 12 and 6789, in order to single out the disjoint cycles, otherwise it would make little sense.

\documentclass{article}
\usepackage{amsmath}
\usepackage{nicematrix}
\begin{document}
Some text to see whether the vertical spacing is good. Some more
text in order to get more than one line. This should be enough.
[
\pi=\left(;\begin{NiceArray}{*{9}{c}}
1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \
2 & 1 & 3 & 4 & 5 & 9 & 6 & 7 & 8
\CodeAfter
  \OverBrace[shorten,yshift=1pt]{1-1}{2-2}{\sigma}
  \OverBrace[shorten,yshift=1pt]{1-6}{2-9}{\tau}
\end{NiceArray};\right)
\smash[b]{\vphantom{%
  \begin{matrix}0\0\0\0\end{matrix}
}}
]
Some text to see whether the vertical spacing is good. Some more
text in order to get more than one line.
\end{document}

Thank you so much, this is perfect! – hugh_maths Jun 30 '23 at 15:20 — hugh_maths, Jun 30 '23 at 15:20

Brackets in a Permutation

1 Answers1