Classical continued fractions for some multivariate polynomials generalizing the Genocchi and median Genocchi numbers

2022/12/14 by Bishal Deb, Alan D. Sokal, Deb, Bishal +1
Computer Science · Mathematics · #05A05 #05A15 #05A19 (Primary) #05A30 #11B68 #30B70 (Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2212.07232

openalex publication_date 2022/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A D-permutation is a permutation of [2n] satisfying 2k-1 ≤ σ(2k-1) and 2k ≥ σ(2k) for all k; they provide a combinatorial model for the Genocchi and median Genocchi numbers. We find Stieltjes-type and Thron-type continued fractions for some multivariate polynomials that enumerate D-permutations with respect to a very large (sometimes infinite) number of simultaneous statistics that measure cycle status, record status, crossings and nestings.

Related

• Continued fractions using a Laguerre digraph interpretation of the Foata--Zeilberger bijection and its variants
• Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions
• Cycles of even-odd drop permutations and continued fractions of Genocchi numbers
• The median Genocchi numbers, Q-analogues and continued fractions
• Equidistributions around special kinds of descents and excedances