Signed words and permutations, IV; Fixed and pixed points

Details Signed words and permutations, IV; Fixed and pixed points Signed words and permutations, IV; Fixed and pixed points

2006-06-23

arxiv.org/abs/math/0606566v1

Mathematics

Combinatorics

21 pages

Scientific paper

The 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.

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