Signed Mahonian polynomials for major and sorting indices

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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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
Pages (from-to)201-226
Number of pages26
JournalJournal of Algebraic Combinatorics
Volume53
Issue number1
DOIs
Publication statusPublished - 2021 Feb

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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