Alternating Eulerian polynomials and left peak polynomials

2021/04/19 by Shi-Mei Ma, Qi Fang, Ma, Shi-Mei +5
Agricultural and Biological Sciences · Mathematics · #05A05 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Botanical Research and Chemistry #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2104.09374

openalex publication_date 2021/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present grammatical interpretations of the alternating Eulerian polynomials of types A and B. As applications, we derive several properties of the type B alternating Eulerian polynomials, including combinatorial expansions, recurrence relations and generating functions. We establish an interesting connection between alternating Eulerian polynomials of type B and left peak polynomials of permutations in the symmetric group, which implies that the type B alternating Eulerian polynomials have gamma-vectors alternate in sign.

Citations

• q-Eulerian Polynomials Arising from Coxeter Groups
• The on-line encyclopedia of integer sequences

Related

• Width-k Eulerian polynomials of type A and B and its Gamma-positivity
• The 1/k-Eulerian polynomials of type B
• The alternating run polynomials of permutations
• Gamma positivity of variations of (α,t)-Eulerian polynomials
• Recurrences for Eulerian polynomials of type B and type D