Degenerate Whitney Numbers of First and Second Kind of Dowling Lattices

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