Creating a staircase shaped tableau

Question

I want to create a tableau of vectors in LaTeX, like the one seen on Slide 7 in these slides.

But unlike in the slides, I want to have vectors like the one given by the code below

\begin{pmatrix}
1\\
0\\
-1
\end{pmatrix}

placed inside the cells. Is there an elegant way to do this, using either TikZ or tables?

Answer 1

The ytableau package could be an option:

\documentclass{article}
\usepackage{amsmath}
\usepackage[boxsize=5em]{ytableau}

\begin{document}

\begin{ytableau}
*(red!20)\begin{pmatrix}1 \\ 0 \\ -1 \end{pmatrix} 
  & *(red!20)\begin{pmatrix}-1 \\ 0 \\ -1 \end{pmatrix} 
  & *(red!20)\begin{pmatrix}0 \\ -1 \\ -1 \end{pmatrix} 
  & *(red!20)\begin{pmatrix}1 \\ -1 \\ 0 \end{pmatrix} 
  & *(red!20)\begin{pmatrix}0 \\ 0 \\ 0 \end{pmatrix} 
  & *(red!20)\begin{pmatrix}1 \\ 1 \\ -1 \end{pmatrix} \\
*(blue!20)\begin{pmatrix}-1 \\ -1 \\ -1 \end{pmatrix} 
  &*(blue!20)\begin{pmatrix}0 \\ 0 \\ -1 \end{pmatrix} 
  & *(blue!20)\begin{pmatrix}1 \\ 1 \\ -1 \end{pmatrix} \\
*(yellow!20)\begin{pmatrix}-1 \\ 0 \\ -1 \end{pmatrix}
  &*(yellow!20)\begin{pmatrix}1 \\ 0 \\ 0 \end{pmatrix}
\end{ytableau}

\end{document}