FACE COUNTING FOR TOPOLOGICAL HYPERPLANE ARRANGEMENTS.

Determining the number of pieces after cutting a cake is a classical problem. Roberts provided an exact solution by computing the number of chambers contained in a plane cut by lines. About 88 years later, Zaslavsky even computed the f-polynomial of a hyperplane arrangement, and consequently deduced the number of chambers of that latter. Recently, Forge and Zaslavsky introduced the more general structure of topological hyperplane arrangements. This article computes the f-polynomial of such arrangements when they are transsective, and therefore deduces their number of chambers. [ABSTRACT FROM AUTHOR]