A generalization of the r-Whitney numbers of the second kind

In this paper, we consider a (p,q)-generalization of the r-Whitney numbers of the second kind and of the associated r-Dowling polynomials. We obtain generalizations of some earlier results for these numbers, including recurrence and generating function formulas, that reduce to them when p=q=1. Furthermore, some of our results appear to be new in the case p=q=1 and thus yield additional formulas for the r-Whitney numbers. As a consequence, some new identities are obtained for the q-Stirling and r-Whitney numbers. In addition, the log-concavity of our generalized Whitney numbers is shown for certain values of the parameters p and q. Finally, we introduce (p,q)-Whitney matrices of the second kind and study some of their properties.