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

摘要

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.