Equi-distribution over descent classes of the hyperoctahedral group

摘要

A classical result of MacMahon shows that the length function and the major index are equi-distributed over the symmetric group. Foata and Schatzenberger 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. (c) 2005 Elsevier Inc. All rights reserved.