The Dowling transform of subspace arrangements

We define the Dowling transform of a real Frame arrangement and show how th e characteristic polynomial changes under this transformation. As a special case, the Dowling transform sends the braid arrangement A(n) to the Dowlin g arrangement. Using Zaslavsky's characterization of supersolvability of si gned graphs, we show supersolvability of an arrangement is preserved under the: Dowling transform. We also give a direct proof of Zaslavsky's result o n the number of chambers and bounded chambers in a real hyperplane arrangem ent. (C) 2000 Academic Press.