ON SUBDIVISIONS OF SIMPLICIAL COMPLEXES - CHARACTERIZING LOCAL H-VECTORS

A well-known combinatorial invariant of simplicial complexes is the h-vector, which has been the subject of much combinatorial research. This paper deals with local h-vectors, recently defined by Stanley as a tool for studying h-vectors of simplicial subdivisions. The face-vector of any simplicial complex can only increase when the complex is subdivided; how does the h-vector change? Motivated by this question, Stanley derived certain useful properties of local h-vectors. In this paper we use mainly geometric arguments to show that these properties characterize local h-vectors, and regular local h-vectors.