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

DOI10.1016/j.aam.2024.102756zbMATH Open1548.0502MaRDI QIDQ6616295

Publication date: 9 October 2024

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Dyck path continued fraction Genocchi numbers Schröder path S-fraction J-fraction T-fraction D-cycle median Genocchi numbers almost-Dyck path D-derangement D-permutation D-semiderangement

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Bernoulli and Euler numbers and polynomials (11B68) Permutations, words, matrices (05A05) Continued fractions; complex-analytic aspects (30B70)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
The median Genocchi numbers, $q$-analogues and continued fractions
Permutations depending on the exceedance type and the number of inversions and combinatorial interpretation of a continued fraction of Heine
A $q$-analog of Schläfli and Gould identities on Stirling numbers
Restricted Dumont permutations, Dyck paths, and noncrossing partitions
Combinatorial aspects of continued fractions
Interpretations combinatoires des nombres de Genocchi
Gandhi $q$-polynomials and Denert statistic
Further results on the Euler and Genocchi numbers
Derangements and Genocchi numbers
On the representation of certain asymptotic series as convergent continued fractions.
On the reduction of a series with decreasing powers of one variable to a continued fraction
Yet another triangle for the Genocchi numbers
Combinatorial proofs of some properties of tangent and Genocchi numbers
On an extension of the Genocchi numbers
Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers
On certain symmetry properties of the Genocchi numbers
Some equidistributed statistics on Genocchi permutations
The Euler and Springer numbers as moment sequences
Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions
Gamma-positivity for a refinement of median Genocchi numbers
The On-Line Encyclopedia of Integer Sequences
Phylogenetic trees, augmented perfect matchings, and a Thron-type continued fraction (T-fraction) for the Ward polynomials
Motzkin paths, Motzkin polynomials and recurrence relations
Comparing two statistical ensembles of quadrangulations: a continued fraction approach
A Survey of Alternating Permutations
A Combinatorial Interpretation of the Seidel Generation of Genocchi Numbers
Denert's Permutation Statistic Is Indeed Euler‐Mahonian
Increasing trees and alternating permutations
The homogenized Linial arrangement and Genocchi numbers
Enumeration of Dumont permutations avoiding certain four-letter patterns
Continued fractions, $q$-Catalan numbers, and $q$-Genocchi 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
Cycles of even-odd drop permutations and continued fractions of Genocchi numbers
A remark on continued fractions for permutations and D-permutations with a weight $-1$ per cycle
A family of polynomials interpolating some classical sequences of numbers

This page was built for publication: Classical continued fractions for some multivariate polynomials generalizing the Genocchi and median Genocchi numbers