Equi-distribution over descent classes of the hyperoctahedral group

Authors:
Ron M. Adin;Francesco Brenti;Yuval Roichman
Affiliations:
Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan, Israel;Dipartimento di Matematica, Universitá di Roma "Tor Vergata", Roma, Italy;Department of Mathematics and Statistics, Bar-Ilan University, Ramat-Gan, Israel
Venue:
Journal of Combinatorial Theory Series A
Year:
2006

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Abstract

A classical result of MacMahon shows that the length function and the major index are equidistributed over the symmetric group. Foata and Schützenberger gave a remarkable refinement and proved that these parameters are equi-distributed over inverse descent classes, implying bivariate equi-distribution identities. Type B analogues of these results, refinements and consequences are given in this paper.