Hankel Transform of (q,r)-Dowling Numbers

Authors

  • Roberto B. Corcino
  • Mary Joy Regidor Latayada Caraga State University
  • Mary Ann Ritzell P. Vega

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i2.3406

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.

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.

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.

Author Biography

Mary Joy Regidor Latayada, Caraga State University

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How to Cite

Corcino, R. B., Latayada, M. J. R., & Vega, M. A. R. P. (2019). Hankel Transform of (q,r)-Dowling Numbers. European Journal of Pure and Applied Mathematics, 12(2), 279–293. https://doi.org/10.29020/nybg.ejpam.v12i2.3406