Finite Rogers-Ramanujan type identities.
Finite vector spaces and certain lattices.
Fonctions symétriques et séries hypergéométriques basiques multivariées
From -Motzkin paths to Schröder paths.
Fully degenerate poly-Bernoulli numbers and polynomials
In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate poly-Bernoulli numbers and polynomials.
General results on the enumeration of strings in Dyck paths.
Généralisation d'identités de Carlitz, Howard et Lehmer.
Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Generalized Cauchy identities, trees and multidimensional Brownian motions. I: Bijective proof of generalized Cauchy identities.
Generalized Eulerian numbers combinatorial applications.
Generalized Schröder matrices arising from enumeration of lattice paths
We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with steps , , , and and not going above the line . We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest. In addition,...
Generalized Schröder numbers and the rotation principle.
Generalizing the combinatorics of binomial coefficients via -nomials.
Generating function for -restricted jagged partitions.
Graphical condensation, overlapping Pfaffians and superpositions of matchings.
Handshakes across a (round) table.
Harmonic number identities via Euler's transform.
Hook length formulas for trees by Han's expansion.
Human proofs of identities by Osburn and Schneider.
Hybrid proofs of the -binomial theorem and other identities.