Equi-distribution over descent classes of the hyperoctahedral group

Ron M. Adin, Francesco Brenti, Yuval Roichman

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8 Scopus citations

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.

Original languageEnglish
Pages (from-to)917-933
Number of pages17
JournalJournal of Combinatorial Theory. Series A
Volume113
Issue number6
DOIs
StatePublished - Aug 2006

Bibliographical note

Funding Information:
✩ The research of the authors was partially supported by the EC’s IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe,” grant HPRN-CT-2001-00272. E-mail addresses: radin@math.biu.ac.il (R.M. Adin), brenti@mat.uniroma2.it (F. Brenti), yuvalr@math.biu.ac.il, yuvalr@macs.biu.ac.il (Y. Roichman).

Keywords

  • Descent class
  • Length
  • Major index
  • Permutation statistics
  • Signed permutations

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