Signed Euler–Mahonian identities

Sen Peng Eu, Zhicong Lin, Yuan Hsun Lo

Research output: Contribution to journalArticle

Abstract

A relationship between signed Eulerian polynomials and the classical Eulerian polynomials on Sn was given by Désarménien and Foata in 1992, and a refined version, called signed Euler–Mahonian identity, together with a bijective proof was proposed by Wachs in the same year. By generalizing this bijection, in this paper we extend the above results to the Coxeter groups of types Bn, Dn, and the complex reflection group G(r,1,n), where the ‘sign’ is taken to be any one-dimensional character. Some obtained identities can be further restricted on some particular set of permutations. We also derive some new interesting sign-balance polynomials for types Bn and Dn.

Original languageEnglish
Article number103209
JournalEuropean Journal of Combinatorics
DOIs
Publication statusAccepted/In press - 2020

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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