Abstract
Let G be a finite group of order m≥1. A Dowling lattice Qn(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 Qn(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.
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