Make all arrow lengths the same in xypic

Question

I'm trying to make all arrows in the following diagram look the same length.

In beamer, the code is as follows:

\documentclass[14pt]{beamer}
\usepackage{xypic}
\begin{document}
\begin{frame}{A visualization of $\mathcal{Q}_n$}
\begin{spacing}{1.5}
\begin{center}
\centerline{\xymatrix@R=1pc@C=0.1em{
&   &                   &      &       \ar[dl](0,n)\ar[dr] &      &        &                                  & &\\
&   &                   &      (0,n-1)\ar[dl]\ar[dr] &                   &     \ar[dl](1,n)\ar[dr]& &      &               & &\\
&   &                   \Ddots\ar[dr]\ar[dl] &       &                   &          & \ddots\ar[dr]\ar[dl] &               & &\\
&   (0,1)\ar[dr]\ar[dl] &      &       & \cdots            &      & &          \ar[dl](n-1,n)\ar[dr]  & &\\
(0,0) &                 &(1,1)           &      &   \cdots     &            &          &       &     (n,n)}}
\end{center}
\end{spacing}
\end{frame}
\end{document}

How can I edit this to make all arrows the same length?

Answer 1

Here is something to start with. The only thing you will have to do is to smash the diagonal dots in order to get them on the same height as the other stuff:

% arara: pdflatex

\documentclass{standalone}
\usepackage{tikz-cd}
\newcommand{\placeholder}{\phantom{(0,n)}}

\begin{document}
\begin{tikzcd}[%
    ,row sep={1cm,between origins}
    ,column sep={1cm,between origins}
    ]
& & & & \ar[dl](0,n)\ar[dr] & & & & \\
& & & (0,n-1)\ar[dl]\ar[dr] & & \ar[dl](1,n)\ar[dr] & & & \\
& & \placeholder\ar[dr]\ar[dl] & & \placeholder & & \placeholder\ar[dr]\ar[dl] & & \\
& (0,1)\ar[dr]\ar[dl] & & \placeholder & \cdots & \placeholder & & \ar[dl](n-1,n)\ar[dr] & \\
(0,0) & & (1,1) & & \cdots & & \placeholder & & (n,n)
\end{tikzcd}
\end{document}

Answer 2

Adding @!0 forces and ignores entry sizes between rows and columns, and then you can make them the size you want, I chose 15mm:

\documentclass{article}
\usepackage[all]{xy}
\begin{document}
\xymatrix@!0@R=15mm@C=15mm{
&&&&\ar[dl](0,n)\ar[dr]&&&&\\
&&&(0,n-1)\ar[dl]\ar[dr]&&\ar[dl](1,n)\ar[dr]&&&\\
&&\Ddots\ar[dr]\ar[dl]&&&&\ddots\ar[dr]\ar[dl]&&\\
&(0,1)\ar[dr]\ar[dl]&&&\cdots&&&\ar[dl](n-1,n)\ar[dr]&\\
(0,0)&&(1,1)&&\cdots&&&&(n,n)}}
\end{document}