2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113989The flag-major index "fmaj" and the classical length function "$\ell$" are used to construct two $q$-analogs of the generating polynomial for the hyperoctahedral group~$B_n$ by number of positive and negative fixed points (resp. pixed points). Specializations of those $q$-analogs are also derived dealing with signed derangements and desarrangements, as well as several classical results that were previously proved for the symmetric group.21 pagesCombinatorics05A15; 05A30; 05E15text