Signed Mahonian polynomials for major and sorting indices

Huilan Chang, Sen Peng Eu, Shishuo Fu, Zhicong Lin, Yuan Hsun Lo

Research output: Contribution to journalArticle

Abstract

We derive some new signed Mahonian polynomials over the complex reflection group G(r, 1 , n) = Cr≀ Sn, where the “sign” is taken to be any of the 2r 1-dim characters and the “Mahonian” statistics are the lmaj defined by Bagno and the sor defined by Eu et al. Various new signed Mahonian polynomials over Coxeter groups of types Bn and Dn are obtained as well. We also investigate the signed counting polynomials on G(r, 1, n) for those statistics with the distribution [r] q[2 r] q⋯ [nr] q.

Original languageEnglish
JournalJournal of Algebraic Combinatorics
DOIs
Publication statusAccepted/In press - 2019 Jan 1
Externally publishedYes

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Keywords

  • Coxeter group
  • Signed Mahonian
  • Sorting index
  • Wreath product

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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