On Flag Vectors, the Dowling Lattice, and Braid Arrangements

Westudycomplexhyperplanearrangementswhoseintersectionlattices,known as the Dowling lattices, are a natural generalization of the partition lattice. We give a combinatorial description of the Dowling lattice via enriched partitions to obtain an explicit EL-labeling and then find a recursion for the flag h-vector in terms of weighted derivations. When the hyperplane arrangements are real they correspond to the braid arrangements An and Bn. By applying a result due to Billera and the authors, we obtain a recursive formula for the cd-index of the lattice of regions of the braid arrangements An and Bn.

• Type: Journal
• Year: 1999
• Where: DCG
• Authors: Richard Ehrenborg, Margaret Readdy
• Keywords: DCG 1999, Dowling Lattice, Natural Generalization, Partition Lattice