Signed Euler–Mahonian identities

Sen Peng Eu, Zhicong Lin, Yuan Hsun Lo

研究成果: 雜誌貢獻期刊論文同行評審

摘要

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.

原文英語
文章編號103209
期刊European Journal of Combinatorics
91
DOIs
出版狀態接受/付印 - 2020

ASJC Scopus subject areas

  • 離散數學和組合

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