Signed Mahonian polynomials for major and sorting indices

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

doi:10.1007/s10801-019-00926-2

Signed Mahonian polynomials for major and sorting indices

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

Department of Mathematics

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

1 Citation (Scopus)

Abstract

We derive some new signed Mahonian polynomials over the complex reflection group G(r, 1 , n) = C_r≀ S_n, 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 B_n and D_n 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 language	English
Pages (from-to)	201-226
Number of pages	26
Journal	Journal of Algebraic Combinatorics
Volume	53
Issue number	1
DOIs	https://doi.org/10.1007/s10801-019-00926-2
Publication status	Published - 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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10.1007/s10801-019-00926-2

Cite this

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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.",

keywords = "Coxeter group, Signed Mahonian, Sorting index, Wreath product",

author = "Huilan Chang and Eu, {Sen Peng} and Shishuo Fu and Zhicong Lin and Lo, {Yuan Hsun}",

note = "Funding Information: The authors would like to express their gratitude to the referees for their valuable comments and suggestions on improving the presentation of this paper. Publisher Copyright: {\textcopyright} 2019, Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Chang, Huilan

AU - Eu, Sen Peng

AU - Fu, Shishuo

AU - Lin, Zhicong

AU - Lo, Yuan Hsun

N1 - Funding Information: The authors would like to express their gratitude to the referees for their valuable comments and suggestions on improving the presentation of this paper. Publisher Copyright: © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2021/2

Y1 - 2021/2

N2 - 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.

AB - 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.

KW - Coxeter group

KW - Signed Mahonian

KW - Sorting index

KW - Wreath product

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Signed Mahonian polynomials for major and sorting indices

Abstract

Keywords

ASJC Scopus subject areas

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