A kind of Eulerian numbers connected to Whitney numbers of Dowling lattices

In 1973 T.A. Dowling constructed a class of geometric lattices with fixed underlying finite groups. Dowling and M. Benoumhani deduced a number of identities satisfied by the Whitney numbers of these lattices. In addition, Remmel and Wachs gave a partition-theoretical interpretation for these numbers. We continue the study of this interpretation introducing an analogue of Eulerian numbers connected to Whitney numbers of the second kind. Moreover, bijective proofs are given for a number of formulas deduced analytically by Benoumhani.