2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113951By a re-examination of MacMahon's original proof of his celebrated theorem on the distribution of the major indices over permutations, we give a reformulation of his argument in terms of the structure of labeled partitions. In this framework, we are able to establish a decomposition theorem for labeled partitions that leads to a simple bijective proof of Wachs' formula on the q-derangement numbers.6 pagesCombinatorics05A30; 05A19, 05A15text