On flag vectors, the Dowling lattice, and braid arrangements

We study complex hyperplane arrangements whose intersection lattices, known as the Dowling lattices, are a natural generalization of the partition lat tice. We give a combinatorial description of the Dowling lattice via enrich ed partitions to obtain an explicit EL-labeling and then find a recursion f or the flag h-vector in terms of weighted derivations. When the hyperplane arrangements are real they correspond to the braid arrangements A, and B-n. By applying a result due to Billera and the authors; we obtain a recursive formula for the ed-index of the lattice of regions of the braid arrangemen ts A(n) and B-n.