On flag vectors, the dowling lattice, and braid arrangements (Q1289241)

Complex hyperplane arrangements whose intersections are Dowling lattices are studied. A combinatorial description of the Dowing lattice via enriched partitions are given. As a result an explicit \(EL\)-labeling and a recursion for the flag \(h\)-vector in terms of weighted derivations are obtained. If the hyperplane arrangements are real they correspond to braid arrangements \(A_n\) and \(B_n.\) By applying a result due to Billera and others a recursive formula for the \(cd\)-index of the lattice of regions of the braid arrangements \(A_n\) and \(B_n\) are found.