2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59089We show that many theorems which assert that two kinds of partitions of the same integer $n$ are equinumerous are actually special cases of a much stronger form of equality. We show that in fact there correspond partition statistics $X$ and $Y$ that have identical distribution functions. The method is an extension of the principle of sieve-equivalence, and it yields simple criteria under which we can infer this identity of distribution functions.Combinatorics05A17text