[Tex/LaTex] Vertical alignment of dots in equation

Question

Consider the following example:

\documentclass{article}

\usepackage{mathtools}

\begin{document}

\begin{alignat*}{6}
                       1 &&                           2 &&                    \ldots &&                           r &&                    \ldots &&                     m & \\
                   m + 1 &&                       m + 2 &&                    \ldots &&                       m + r &&                    \ldots &&                    2m & \\
                  2m + 1 &&                      2m + 2 &&                    \ldots &&                      2m + r &&                    \ldots &&                    3m & \\
  \vdotswithin{(n-1)m+1} &&      \vdotswithin{(n-1)m+2} &&      \vdotswithin{\ldots} &&      \vdotswithin{(n-1)m+r} &&      \vdotswithin{\ldots} &&      \vdotswithin{nm} & \\
            (n - 1)m + 1 &&\quad           (n - 1)m + 2 &&\quad               \ldots &&\quad           (n - 1)m + r &&\quad               \ldots &&\quad               nm &
\end{alignat*}

\end{document}

As can be seen, the vertical dots are not perfectly centered relative to the longest entry in each column; they are a little to the left of the center. How do I fix this?

Answer 1

The \ldots is defined as \mathinner which adds surrounding space. When used in this context the extra space after is removed. Inside \vdotswithin it is treated as {}\ldots{} which ensure that the surrounding spaces are preserved.

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{alignat*}{6}
                       1 &&                           2 &&                {}\ldots{} &&                           r &&                {}\ldots{}&&                     m & \\
                   m + 1 &&                       m + 2 &&                {}\ldots{} &&                       m + r &&                {}\ldots{}&&                    2m & \\
                  2m + 1 &&                      2m + 2 &&                {}\ldots{} &&                      2m + r &&                {}\ldots{}&&                    3m & \\
  \vdotswithin{(n-1)m+1} &&      \vdotswithin{(n-1)m+2} &&     \vdotswithin{\ldots}  &&      \vdotswithin{(n-1)m+r} &&     \vdotswithin{\ldots} &&      \vdotswithin{nm} & \\
            (n - 1)m + 1 &&\quad           (n - 1)m + 2 &&\quad           {}\ldots{} &&\quad           (n - 1)m + r &&\quad           {}\ldots{} &&\quad               nm &
\end{alignat*}
\end{document}