Equi-distribution over Descent Classes of the Hyperoctahedral Group
Combinatorics
2007-05-23 v4 Group Theory
Abstract
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 analogues of these results, refinements and consequences are given in this paper.
Keywords
Cite
@article{arxiv.math/0508362,
title = {Equi-distribution over Descent Classes of the Hyperoctahedral Group},
author = {R. M. Adin and F. Brenti and Y. Roichman},
journal= {arXiv preprint arXiv:math/0508362},
year = {2007}
}
Comments
23 pp., to appear in J. Combin. Theory (Ser. A); reference added in proof