Signed words and permutations, IV: Fixed and pixed points

Abstract

The flag-major index “fmaj” and the classical length function “ℓ” 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.