Signed mahonian identities on permutations with subsequence restrictions

Eu, Sen Peng; Fu, Tung-Shan; Hsu, Hsiang Chun; Liao, Hsin Chieh; Sun, Wei

doi:10.1016/j.jcta.2019.105131

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…Extended Insertion Lemma. Eu et al [10,Theorem 1.3] derived the generating polynomial for the increment of major index with sign resulting from inserting an additional pair of consecutive elements in any place of a given permutation.…”

Section: By (I) and Induction Hypothesismentioning

confidence: 99%

“…Specifically, for r = 1 and the sign character χ −1,0 (σ) = (−1) inv(σ) , we derive the following results from Theorems 2.2 and 2.3, which have been established in [10,Theorem 1.2]. We make use of the notation [n] ±q !…”

Section: Note That Inmentioning

confidence: 99%

“…, n) as a subsequence. Eu et al derived broader results on the permutations with varied subsequence restrictions [10,Theorem 1.2], and suggested extending the results further to the signed permutation group B n , in the spirit of [9,Problem 5.9].…”

Section: Introductionmentioning

confidence: 99%

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Signed Mahonian on Parabolic Quotients of Colored Permutation Groups

Eu¹,

Fu²,

Lo³

2020

Preprint

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We study the generating polynomial of the flag major index with each onedimensional character, called signed Mahonian polynomial, over the colored permutation group, the wreath product of a cyclic group with the symmetric group. Using the insertion lemma of Han and Haglund-Loehr-Remmel and a signed extension established by Eu et al., we derive the signed Mahonian polynomial over the quotients of parabolic subgroups of the colored permutation group, for a variety of systems of coset representatives in terms of subsequence restrictions. This generalizes the related work over parabolic quotients of the symmetric group due to Caselli as well as to Eu et al. As a byproduct, we derive a product formula that generalizes Biagioli's result about the signed Mahonian on the even signed permutation groups.

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Section: By (I) and Induction Hypothesismentioning

confidence: 99%

Section: Note That Inmentioning

confidence: 99%

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Signed Mahonian on Parabolic Quotients of Colored Permutation Groups

Eu¹,

Fu²,

Lo³

2020

Preprint

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“…• From symmetric group to other reflection groups by Reiner [27], Adin-Gessel-Roichman [1], Biagioli [6], Biagioli-Caselli [8] and Chang-Eu-Fu-Lin-Lo [12], to name a few. • To restricted permutations such as 321-avoiding permutations by Adin-Roichman [3] and Eu-Fu-Pan-Ting [15], Simsun permutations by Eu-Fu-Pan [14], PRW permutations by Lin-Wang-Zeng [22] and permutations with subsequence restrictions by Eu-Fu-Hsu-Liao-Sun [16].…”

Section: Introductionmentioning

confidence: 99%

Signed Euler-Mahonian identities

Eu¹,

Zhao²,

Lo³

2020

Preprint

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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 were 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.

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Signed Mahonian on parabolic quotients of colored permutation groups

2022

Advances in Applied Mathematics

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Signed mahonian identities on permutations with subsequence restrictions

Cited by 5 publications

References 8 publications

Signed Mahonian on Parabolic Quotients of Colored Permutation Groups

Signed Mahonian on Parabolic Quotients of Colored Permutation Groups

Signed Euler-Mahonian identities

Signed Mahonian on parabolic quotients of colored permutation groups

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