Equi-distribution over Descent Classes of the Hyperoctahedral Group

2005/08/19 by R. M. Adin, Ron M. Adin, Francesco Brenti +6
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #graph theory and CDMA systems #math.CO #math.GR #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0508362

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

arxiv created 2005/09/06 · arxiv updated 2009/12/01

Abstract

A classical result of MacMahon shows that the length function and the major index are equi-distributed 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.

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