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Dowling constructed Dowling lattice Qn(G), for any finite set with n elementsand any finite multiplicative group G of order m, which is a finite geometriclattice. He also defined the Whitney numbers of the first and second kinds forany finite geometric lattice. These numbers for the Dowling lattice Qn(G) arethe Whitney numbers of the first kind Vm(n,k) and those of the second kindWm(n,k), which are given by Stirling number-like relations. In this paper, by`degenerating' such relations we introduce the degenerate Whitney numbers ofthe first kind and those of the second kind and investigate, among otherthings, generating functions, recurrence relations and various explicitexpressions for them. As further generalizations of the degenerate Whitneynumbers of both kinds, we also consider the degenerate r-Whitney numbers ofboth kinds.

A Study on degenerate Whitney numbers of the first and second kinds of Dowling lattices