Derivative polynomials and enumeration of permutations by their alternating descents

2015/04/09 by Shi-Mei Ma, Ma, Shi-Mei, Yeong‐Nan Yeh +1 · 1 citation
Mathematics · #05A15 #26C10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1504.02372

openalex publication_date 2015/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present an explicit formula for the number of permutations with a given number of alternating descents. Moreover, we study the interlacing property of the real parts of the zeros of the generating polynomials of these numbers.

Cited by

• An asymptotic distribution theory for Eulerian recurrences with applications

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• A new combinatorial formula for alternating descent polynomials
• Alternating runs of permutations and the central factorial numbers
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• Permutations with Extremal number of Fixed Points