Monotonic matrix

In combinatorics, a monotonic matrix of size n is a square matrix of size n with entries in the set of integers ${\displaystyle \{0,1,\dots ,n\}}$ such that

1. the nonzero entries in each row are strictly increasing from left to right,
2. the nonzero entries in each column are strictly decreasing from top to bottom, and
3. (positive slope condition) for two nonzero cells of the same entry, the one further right is placed higher than the early one.

Equivalently, a square matrix with integer entries is monotonic if the corresponding semicrosses are disjoint.[1]

An example is:

${\displaystyle {\begin{bmatrix}2&&3\\&&1\\1&3&\\\end{bmatrix}}}$.