Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.5

Some Theorems and Applications of the (q,r)-Whitney Numbers

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


The (q,r)-Whitney numbers were recently defined in terms of the q-Boson operators, and several combinatorial properties which appear to be q-analogues of similar properties were studied. In this paper, we obtain elementary and complete symmetric polynomial forms for the (q,r)-Whitney numbers, and give combinatorial interpretations in the context of A-tableaux. We also obtain convolution-type identities using the combinatorics of A-tableaux. Lastly, we present applications and theorems related to discrete q-distributions.

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(Concerned with sequences A000110 A003575 A008275 A008277.)

Received August 16 2016; revised versions received November 20 2016; November 21 2016. Published in Journal of Integer Sequences, December 27 2016.

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