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