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arXiv · 1709.07999

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

Mahid M. Mangontarum
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Abstract

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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Mahid M. Mangontarum. 2017-09-23. Some Theorems and Applications of the $(q,r)$-Whitney Numbers. https://arxiv.org/abs/1709.07999

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