Signed Mahonians

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

doi:10.1016/j.jcta.2004.07.006

Signed Mahonians

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

Department of Mathematics

Brandeis University

Research output: Contribution to journal › Article › peer-review

22 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 language	English
Pages (from-to)	25-43
Number of pages	19
Journal	Journal of Combinatorial Theory. Series A
Volume	109
Issue number	1
DOIs	https://doi.org/10.1016/j.jcta.2004.07.006
State	Published - 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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10.1016/j.jcta.2004.07.006

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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.",

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KW - Permutation statistics

KW - Signed generating function

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Signed Mahonians

Abstract

Bibliographical note

Keywords

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