KöMaL 2025 B5442

Let $n$, $k$ and $\ell$ denote positive integers, and let $g(n,k,\ell)$ denote the number of ways that an $n\times k$ table can be filled with the elements of $\{1,2,\ldots, {\ell+1}\}$ such that in each row from left to right and in each column from top to bottom the numbers are monotonously increasing. Prove that $g(n,k,\ell)=g(k,\ell,n)$.