Context-free grammars for several polynomials associated with Eulerian polynomials

2016/09/19 by Shi-Mei Ma, Ma, Shi-Mei, Jun Ma +6
Computer Science · Mathematics · #05A05 #05A15 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:05A15 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1609.05829

14 pages

arxiv created 2016/09/19 · openalex publication_date 2016/09/19 · arxiv updated 2016/09/20 · openalex created_date 2016/09/30 · openalex updated_date 2026/07/28

Abstract

In this paper, we present grammatical descriptions of several polynomials associated with Eulerian polynomials, including q-Eulerian polynomials, alternating run polynomials and derangement polynomials. As applications, we get several convolution formulas involving these polynomials.

Citations

• q-Eulerian Polynomials Arising from Coxeter Groups
• Eulerian polynomials, perfect matchings and Stirling permutations of the second kind

Related

• The Dumont Ansatz for the Eulerian Polynomials, Peak Polynomials and Derivative Polynomials
• Bessel polynomials, double factorials and context-free grammars
• Alternating Eulerian polynomials and left peak polynomials
• A Context-free Grammar for the e-Positivity of the Trivariate Second-order Eulerian Polynomials
• General Eulerian Numbers and Eulerian Polynomials