On the descent polynomial of signed multipermutations

Zhao, Lin

doi:10.1090/s0002-9939-2015-12555-5

Cited by 13 publications

(9 citation statements)

References 13 publications

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“…Recently, Lin [46] considered the descent polynomials on signed permutations of the general multiset M s := {1 s 1 , 2 s 2 , . .…”

Section: Descent Polynomials On Signed Permutations Of the 2-multisetmentioning

confidence: 99%

Stability of combinatorial polynomials and its applications

Ding,

Zhu

2021

Preprint

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Many important problems are closely related to the zeros of certain polynomials derived from combinatorial objects. The aim of this paper is to make a systematical study on the stability of polynomials in combinatorics.Applying the characterizations of Borcea and Brändén concerning linear operators preserving stability, we present criteria for real stability and Hurwitz stability of recursive polynomials. We also give a criterion for Hurwitz stability of the Turán

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“…Recently, Lin [46] considered the descent polynomials on signed permutations of the general multiset M s := {1 s 1 , 2 s 2 , . .…”

Section: Descent Polynomials On Signed Permutations Of the 2-multisetmentioning

confidence: 99%

Stability of combinatorial polynomials and its applications

Ding,

Zhu

2021

Preprint

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“…The proof is based on the technique of flag barred permutations developed by the second named author [21], which was originally inspired by Gessel and Stanley [19]. We need some preparations.…”

Section: Coxeter Groups Of Type B Nmentioning

confidence: 99%

“…For instance, for π = 13 42 5 ∈ B 5 , we have δ π = 01011 and ch(π) = 3. It was shown in [21,Lemma 17] that…”

Section: Coxeter Groups Of Type B Nmentioning

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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“…Our proof of Theorem 4.1 adopts the method of 'balls in boxes'. For more information about this method, see [21][22][23]. Before giving the proof, let us first introduce some notations and definitions.…”

Section: Proof Of Theorem 36mentioning

confidence: 99%

Interlacing polynomials and the veronese construction for rational formal power series

Zhang¹

2019

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Fixing a positive integer r and 0 ≤ k ≤ r − 1, define f r,k for every formal power series f as f (x) = f r,0 (x r ) + xf r,1 (x r ) + · · · + x r−1 f r,r−1 (x r ). Jochemko recently showed that the polynomial U n r,k h(x) := ((1 + x + · · · + x r−1 ) n h(x)) r,k has only nonpositive zeros for any r ≥ deg h(x) − k and any positive integer n. As a consequence, Jochemko confirmed a conjecture of Beck and Stapledon on the Ehrhart polynomial h(x) of a lattice polytope of dimension n, which states that U n r,0 h(x) has only negative, real zeros whenever r ≥ n. In this paper, we provide an alternative approach to Beck and Stapledon's conjecture by proving the following general result: if the polynomial sequence. Our result has many other interesting applications. In particular, this enables us to give a new proof of Savage and Visontai's result on the interlacing property of some refinements of the descent generating functions for colored permutations. Besides, we derive a Carlitz identity for refined colored permutations.

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On the descent polynomial of signed multipermutations

Cited by 13 publications

References 13 publications

Stability of combinatorial polynomials and its applications

Stability of combinatorial polynomials and its applications

Signed Euler-Mahonian identities

Interlacing polynomials and the veronese construction for rational formal power series

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