The Dowling transform of subspace arrangements (Q1584659)

The paper introduces the Dowling transform, which takes a real frame arrangement with coordinate hyperplanes into a complex one. The Dowling transform takes the braid arrangement \(A_n\) to the Dowling arrangement. It is shown that the Dowling transform preserves supersolvability. A direct proof is given to Zaslavsky's theorem, which counts the chambers and bounded chambers of a real hyperplane arrangement in terms of the characteristic polynomial of the arrangement.