2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73366We discuss permutation representations which are obtained by the natural action of $S_n \times S_n$ on some special sets of invertible matrices, defined by simple combinatorial attributes. We decompose these representations into irreducibles. The multiplicities involved have a nice combinatorial interpretation. We also generalize known results on asymptotic behavior of the conjugacy representation of $S_n$.Representation TheoryCombinatoricstext