Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions

2022/03/17 by Alan D. Sokal, Jiang Zeng · 3 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Mathematical functions and polynomials

paper · doi:10.1016/j.aam.2022.102341

Abstract

We find Stieltjes-type and Jacobi-type continued fractions for some “master polynomials” that enumerate permutations, set partitions or perfect matchings with a large (sometimes infinite) number of simultaneous statistics. Our results contain many previously obtained identities as special cases, providing a common refinement of all of them.

Citations

• Denert's Permutation Statistic Is Indeed Euler‐Mahonian
• Nombres Exponentiels Et Nombres De Bernoulli

Cited by

• Classical continued fractions for some multivariate polynomials generalizing the Genocchi and median Genocchi numbers
• Parity patterns meet Genocchi numbers, I: four labelings and three bijections
• Continued fractions using a Laguerre digraph interpretation of the Foata--Zeilberger bijection and its variants

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• Continued fractions using a Laguerre digraph interpretation of the Foata--Zeilberger bijection and its variants
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• Restricted set of patterns, continued fractions, and Chebyshev polynomials
• Lattice paths and branched continued fractions: An infinite sequence of generalizations of the Stieltjes--Rogers and Thron--Rogers polynomials, with coefficientwise Hankel-total positivity