Alternating Eulerian polynomials and left peak polynomials

被引：7

作者：

Ma, Shi-Mei ^{[1
]}

Fang, Qi ^{[2
]}

Mansour, Toufik ^{[3
]}

Yeh, Yeong-Nan ^{[4
]}

机构：

[1] Northeastern Univ Qinhuangdao, Sch Math & Stat, Qinhuangdao 066004, Hebei, Peoples R China

[2] Northeastern Univ, Dept Math, Shenyang 110004, Peoples R China

[3] Univ Haifa, Dept Math, IL-3498838 Haifa, Israel

[4] Wenzhou Univ, Coll Math & Phys, Wenzhou 325035, Peoples R China

来源：

DISCRETE MATHEMATICS | 2022年 / 345卷 / 03期

关键词：

Eulerian polynomials; Alternating descents; Left peaks; Gamma-vectors; CONTEXT-FREE GRAMMARS; DERIVATIVE POLYNOMIALS; PERMUTATIONS; ENUMERATION; TANGENT; NUMBERS; SNAKES;

D O I：

10.1016/j.disc.2021.112714

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：12

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