A new combinatorial formula for alternating descent polynomials

2022/07/13 by Qiongqiong Pan, Pan, Qiongqiong
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2207.06212

openalex publication_date 2022/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a combinatorial formula for the alternating descent polynomials of type A and B. Combining with Josuat-Vergès' combinatorial interpretation for Hoffman's derivative polynomials for tangent and secant functions, we obtain a unified combinatorial proof of Ma-Yeh's two formulae linking these two families of polynomials.

Related

• Derivative polynomials and enumeration of permutations by their alternating descents
• Recurrences for the derivative polynomials for tangent and secant
• Positivity and divisibility of alternating descent polynomials
• A family of two-variable derivative polynomials for tangent and secant
• A Generalization of Descent Polynomials