r-Whitney numbers of Dowling lattices

Let G be a finite group of order m >= 1. A Dowling lattice Q(n)(G) is the geometric lattice of rank n over G. In this paper, we define the r-Whitney numbers of the first and second kind over Q(n)(G), respectively. This concept is a common generalization of the Whitney numbers and the r-Stirling numbers of both kinds. We give their combinatorial interpretations over the Dowling lattice and we obtain various new algebraic identities. In addition, we develop the r-Whitney-Lah numbers and the r-Dowling polynomials associated with the Dowling lattice. (C) 2012 Elsevier B.V. All rights reserved.