Journal of Integer Sequences, Vol. 18 (2015), Article 15.9.8

On q-Boson Operators and q-Analogues of the r-Whitney and r-Dowling Numbers

Mahid M. Mangontarum
Department of Mathematics
Mindanao State University – Main Campus
Marawi City 9700

Jacob Katriel
Department of Chemistry
Technion – Israel Institute of Technology
Haifa 32000


We define the (q, r)-Whitney numbers of the first and second kinds in terms of the q-Boson operators, and obtain several fundamental properties such as recurrence formulas, orthogonality and inverse relations, and other interesting identities. As a special case, we obtain a q-analogue of the r-Stirling numbers of the first and second kinds. Finally, we define the (q, r)-Dowling polynomials in terms of sums of (q, r)-Whitney numbers of the second kind, and obtain some of their properties.

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(Concerned with sequences A000110 A003575 A008275 A008277.)

Received May 13 2015; revised version received, September 1 2015. Published in Journal of Integer Sequences, September 7 2015.

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