Signed words and permutations, IV; Fixed and pixed points

2006/06/23 by Foata, Dominique, Han, Guo-Niu
#05A15 #05A30 #05E15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0606566

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.

Related

• Barycentric subdivisions and derangement polynomials for the even-signed permutation groups
• Proof of Stasinski and Voll's Hyperoctahedral Group Conjecture
• Number of permutations with same peak set for signed permutations
• A new statistic on the hyperoctahedral groups
• Character formulas and descents for the hyperoctahedral group