Alternating Eulerian polynomials and left peak polynomials

Shi Mei Ma; Qi Fang; Toufik Mansour; Yeong Nan Yeh

doi:10.1016/j.disc.2021.112714

Alternating Eulerian polynomials and left peak polynomials

Shi Mei Ma
, Qi Fang
, Toufik Mansour
, Yeong Nan Yeh

Department of Mathematics

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

Abstract

We first present grammatical interpretations for the alternating Eulerian polynomials of types A and B. As applications, we then derive several properties of the type B alternating Eulerian polynomials, including recurrence relations, generating function and unimodality. And then, we establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials, which implies that the type B alternating Eulerian polynomials have gamma-vectors that alternate in sign.

Original language	English
Article number	112714
Journal	Discrete Mathematics
Volume	345
Issue number	3
DOIs	https://doi.org/10.1016/j.disc.2021.112714
State	Published - Mar 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Alternating descents
Eulerian polynomials
Gamma-vectors
Left peaks

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2021.112714

Cite this

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title = "Alternating Eulerian polynomials and left peak polynomials",

abstract = "We first present grammatical interpretations for the alternating Eulerian polynomials of types A and B. As applications, we then derive several properties of the type B alternating Eulerian polynomials, including recurrence relations, generating function and unimodality. And then, we establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials, which implies that the type B alternating Eulerian polynomials have gamma-vectors that alternate in sign.",

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AU - Fang, Qi

AU - Mansour, Toufik

AU - Yeh, Yeong Nan

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Y1 - 2022/3

N2 - We first present grammatical interpretations for the alternating Eulerian polynomials of types A and B. As applications, we then derive several properties of the type B alternating Eulerian polynomials, including recurrence relations, generating function and unimodality. And then, we establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials, which implies that the type B alternating Eulerian polynomials have gamma-vectors that alternate in sign.

AB - We first present grammatical interpretations for the alternating Eulerian polynomials of types A and B. As applications, we then derive several properties of the type B alternating Eulerian polynomials, including recurrence relations, generating function and unimodality. And then, we establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials, which implies that the type B alternating Eulerian polynomials have gamma-vectors that alternate in sign.

KW - Alternating descents

KW - Eulerian polynomials

KW - Gamma-vectors

KW - Left peaks

UR - https://www.scopus.com/pages/publications/85119174216

U2 - 10.1016/j.disc.2021.112714

DO - 10.1016/j.disc.2021.112714

M3 - Article

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SN - 0012-365X

VL - 345

JO - Discrete Mathematics

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Alternating Eulerian polynomials and left peak polynomials

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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