Hankel Transform of (q,r)-Dowling Numbers

Roberto B. Corcino, Mary Joy Regidor Latayada, Mary Ann Ritzell P. Vega

Abstract

In this paper, we establish certain combinatorial interpretation for $q$-analogue of $r$-Whitney numbers of the second kind defined by Corcino and Ca\~{n}ete in the context of $A$-tableaux. We derive convolution-type identities by making use of the combinatorics of $A$-tableaux. Finally, we define a $q$-analogue of $r$-Dowling numbers and obtain some necessary properties including its Hankel transform.

Keywords

{$r$-Whitney numbers, $r$-Dowling numbers, generating function, $q$-analogue, $q$-exponential function, $A$-tableau, convolution formula, Hankel transform, Hankel matrix, $k$-binomial transform.

Full Text:

PDF