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

Access to Document

10.1016/j.disc.2021.112714

Cite this

@article{2e28ba2381a648a49f9776ea1c2382b9,

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.",

keywords = "Alternating descents, Eulerian polynomials, Gamma-vectors, Left peaks",

author = "Ma, {Shi Mei} and Qi Fang and Toufik Mansour and Yeh, {Yeong Nan}",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2022",

month = mar,

doi = "10.1016/j.disc.2021.112714",

language = "English",

volume = "345",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "3",

}

TY - JOUR

T1 - Alternating Eulerian polynomials and left peak polynomials

AU - Ma, Shi Mei

AU - Fang, Qi

AU - Mansour, Toufik

AU - Yeh, Yeong Nan

PY - 2022/3

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 - http://www.scopus.com/inward/record.url?scp=85119174216&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2021.112714

DO - 10.1016/j.disc.2021.112714

M3 - Article

AN - SCOPUS:85119174216

SN - 0012-365X

VL - 345

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 3

M1 - 112714

ER -

Alternating Eulerian polynomials and left peak polynomials

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this