A $q$-analogue of Qi formula for $r$-Dowling numbers
Commun. Korean Math. Soc. 2020 Vol. 35, No. 1, 21-41
Published online January 31, 2020
Joy Antonette D. Cillar, Roberto B. Corcino
University of San Jose-Recoletos; Cebu Normal University
Abstract : In this paper, we establish an explicit formula for $r$-Dowling numbers in terms of $r$-Whitney Lah and $r$-Whitney numbers of the second kind. This is a generalization of the Qi formula for Bell numbers in terms of Lah and Stirling numbers of the second kind. Moreover, we define the $q,r$-Dowling numbers, $q,r$-Whitney Lah numbers and $q,r$-Whitney numbers of the first kind and obtain several fundamental properties of these numbers such as orthogonality and inverse relations, recurrence relations, and generating functions. Hence, we derive an analogous Qi formula for $q,r$-Dowling numbers expressed in terms of $q,r$-Whitney Lah numbers and $q,r$-Whitney numbers of the second kind.
Keywords : $r$-Dowling numbers, $r$-Whitney numbers, Lah numbers, recurrence relation, explicit formula, generating function, $q$-analogue
MSC numbers : 05A10, 05A15, 11B65, 11B73
Downloads: Full-text PDF   Full-text HTML


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd