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

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
Journal	Journal of Algebraic Combinatorics
DOIs	https://doi.org/10.1007/s10801-019-00926-2
Publication status	Accepted/In press - 2019 Jan 1

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

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Chang, H., Eu, S. P., Fu, S., Lin, Z., & Lo, Y. H. (Accepted/In press). Signed Mahonian polynomials for major and sorting indices. Journal of Algebraic Combinatorics. https://doi.org/10.1007/s10801-019-00926-2

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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}",

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T1 - Signed Mahonian polynomials for major and sorting indices

AU - Chang, Huilan

AU - Eu, Sen Peng

AU - Fu, Shishuo

AU - Lin, Zhicong

AU - Lo, Yuan Hsun

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Y1 - 2019/1/1

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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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