Equi-distribution over Descent Classes of the Hyperoctahedral Group

Details Equi-distribution over Descent Classes of the Hyperoctahedral Group Equi-distribution over Descent Classes of the Hyperoctahedral Group

2005-08-19

arxiv.org/abs/math/0508362v4

Mathematics

Combinatorics

23 pp., to appear in J. Combin. Theory (Ser. A); reference added in proof

Scientific paper

A classical result of MacMahon shows that the length function and the major index are equi-distributed over the symmetric group. Foata and Sch\"utzenberger 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.

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