2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70152A classical result of MacMahon gives a simple product formula for the generating function of major index over the symmetric group. A similar factorial-type product formula for the generating function of major index together with sign was given by Gessel and Simion. Several extensions are given in this paper, including a recurrence formula, a specialization at roots of unity and type $B$ analogues.23 pagesCombinatoricstext