A new refinement of Euler numbers on counting alternating permutations

2019/08/02 by Masato Kobayashi, Kobayashi, Masato
Mathematics · #2010 Primary:05A05 Secondary:11B68 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1908.00701

openalex publication_date 2019/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

At a crossroads of calculus and combinatorics, the generating function of secant and tangent numbers (Euler numbers) provides enumeration of alternating permutations. In this article, we present a new refinement of Euler numbers to answer the combinatorial question on some particular relation of Euler numbers proved by Heneghan-Petersen, Power series for up-down min-max permutations, College Math. Journal, Vol. 45, No. 2 (2014), 83-91.

Related

• A Survey of Alternating Permutations
• Signed Countings of types B and D permutations and t,q-Euler Numbers
• Counting permutations by alternating descents
• Generalized Eulerian Numbers
• Signed Countings of Type B and D Permutations and t,q-Euler numbers