rr-Whitney numbers of Dowling lattices

Let GG be a finite group of order m≥1m≥1. A Dowling lattice Qn(G)Qn(G) is the geometric lattice of rank nn over GG. In this paper, we define the rr-Whitney numbers of the first and second kind over Qn(G)Qn(G), respectively. This concept is a common generalization of the Whitney numbers and the rr-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 rr-Whitney–Lah numbers and the rr-Dowling polynomials associated with the Dowling lattice.