How can I have a brace on the left and the top of a matrix without overlapping?

Question

Consider the following code:

\documentclass{article}

\usepackage{amsmath}
\usepackage{rotating}

\begin{document}

\begin{align*}
  \rotatebox[origin=c]{90}{$n$ parts}\left\{\overbrace{\begin{matrix}
    \bullet & \bullet & \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \cdots & \bullet\\
    \bullet & \cdots & \bullet\\
  \end{matrix}}^{\text{Even number}}\right.
\end{align*}

\begin{align*}
  \rotatebox[origin=c]{90}{$n$ parts}\overbrace{\left\{\begin{matrix}
    \bullet & \bullet & \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \cdots & \bullet\\
    \bullet & \cdots & \bullet\\
  \end{matrix}\right.}^{\text{Even number}}
\end{align*}

\end{document}

This produces the following output:

In both cases, one of the braces overlaps the other. I'd like to be able to have each brace start and end exactly at one of the dots in the diagram. How can I go about accomplishing this?

Answer 1

Here’s one way you could do it:

\documentclass{article}

\usepackage{amsmath}
\usepackage{rotating}

\begin{document}

\begin{equation*}
  %
  % the vertical brace
  %
  \rotatebox[origin=c]{90}{\scriptsize{
    $n$ parts
  }}
  %
  % an invisible matrix for height
  %
  \left\{\begin{matrix}
     \vphantom{} \\ \vphantom{} \\ \vphantom{} \\
     \vphantom{} \\ \vphantom{} \\ \vphantom{} \\
  \end{matrix}\right.
  %
  % the horizontal brace and the visible matrix
  %
  \overbrace{
    \begin{matrix}
      \bullet & \bullet & \bullet & \bullet & \bullet & \cdots & \bullet\\
      \bullet & \bullet & \bullet & \cdots & \bullet\\
      \bullet & \bullet & \bullet & \cdots & \bullet\\
      \bullet & \bullet & \bullet & \cdots & \bullet\\
      \bullet & \cdots & \bullet\\
      \bullet & \cdots & \bullet\\
    \end{matrix}
  }^{\text{
    even number
  }}
\end{equation*}

\end{document}

which looks like

This is very similar to your examples, with only one difference: the two braces are now wrapping around different matrices.

The matrix whose entries are all \vphantom{} doesn’t show up in the printed document, but it has the same height as the matrix of dots. If you made the dot matrix bigger or smaller, you’d need to add or remove entries from this matrix to compensate. This matrix provides the size for the vertical brace.

Then the horizontal brace wraps around the original dot matrix, and never sees the space occupied by the vertical brace.

---

Alternatively, here’s a fairly simple TikZ-based solution that uses the matrix library to lay out the entries, and then the decorations library to draw the braces.

\documentclass{article}

\usepackage{amsmath}
\usepackage{rotating}
\usepackage{tikz}

\usetikzlibrary{matrix, decorations.pathreplacing}

\begin{document}

\begin{tikzpicture}[decoration={brace, amplitude=6pt}]
    \matrix (m) [matrix of math nodes] {
      \bullet & \bullet & \bullet & \bullet & \bullet & \cdots & \bullet\\
      \bullet & \bullet & \bullet & \cdots & \bullet\\
      \bullet & \bullet & \bullet & \cdots & \bullet\\
      \bullet & \bullet & \bullet & \cdots & \bullet\\
      \bullet & \cdots & \bullet\\
      \bullet & \cdots & \bullet\\
    };
    \draw [decorate, transform canvas={xshift=-0.3em}, thick]
           (m-6-1.south west) -- node [left=6pt]
           {\rotatebox[origin=c]{90}{\scriptsize\text{$n$ parts}}} (m-1-1.north west);
    \draw [decorate, transform canvas={yshift=0.5em, xshift=0.5em}, thick]
          (m-1-1.north west) -- node [above=6pt]
          {\scriptsize\text{even number}} (m-1-6.north east);
\end{tikzpicture}

\end{document}

This is what the TikZ solution looks like:

Answer 2

Here's how you can do it with stacks:

\documentclass{article}
\usepackage{tabstackengine}
\stackMath
\begin{document}
\setbox0=\hbox{\setstacktabbedgap{1ex}\tabbedCenterstack{
    \bullet & \bullet & \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \bullet & \bullet & \cdots & \bullet\\
    \bullet & \cdots & \bullet\\
    \bullet & \cdots & \bullet
}}
\[
\Shortstack[r]{%
  {\stackon{\makebox[\wd0]{\downbracefill}}{\textrm{top~text}}}\\
  {\textrm{side~text}\left\{\box0\right.}
}
\]
\end{document}

Answer 3

Here is what you can do with {NiceMatrix} of nicematrix (≥ 6.4 of 2021-11-23):

\documentclass{article}
\usepackage{nicematrix}
\begin{document}
$\begin{NiceMatrix}
  \Block{*-1}{\rotate n \text{ parts}}
  & \bullet & \bullet & \bullet & \bullet & \bullet & \cdots & \bullet\
  & \bullet & \bullet & \bullet & \cdots & \bullet\
  & \bullet & \bullet & \bullet & \cdots & \bullet\
  & \bullet & \bullet & \bullet & \cdots & \bullet\
  & \bullet & \cdots & \bullet\
  & \bullet & \cdots & \bullet\
\CodeAfter
  \OverBrace{1-2}{1-last}{\text{even number}}[yshift=1mm]
  \SubMatrix{{}{1-2}{last-2}{.}[left-xshift=0.8mm]
\end{NiceMatrix}$
\end{document}

You need several compilations (because nicematrix uses PGF/Tikz nodes under the hood).