Signed Mahonians

Ron M. Adin, Ira M. Gessel, Yuval Roichman

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

A classical result of MacMahon gives a simple product formula for the generating function of major index over the symmetric group. A similar factorial-type product formula for the generating function of major index together with sign was given by Gessel and Simion. Several extensions are given in this paper, including a recurrence formula, a specialization at roots of unity and type B analogues.

Original languageEnglish
Pages (from-to)25-43
Number of pages19
JournalJournal of Combinatorial Theory. Series A
Volume109
Issue number1
DOIs
StatePublished - Jan 2005

Bibliographical note

Funding Information:
RonM.AdinandYuvalRoichmanwerepartiallysupportedbytheEC’sIHRPProgramme, within the Research Training Network “Algebraic Combinatorics in Europe”, Grant HPRN-CT-2001-00272. Ira M. Gessel was partially supported by NSF Grant DMS-0200596.

Keywords

  • Flag major index
  • Major index
  • Permutation statistics
  • Signed generating function

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