CONVEX HULLS OF F-VECTOR AND BETA-VECTOR

In this paper we describe the convex hulls of the sets of f- and beta- vectors of different classes of simplicial complexes on n vertices. Th ese include flag complexes, order complexes of posets, matroid complex es, and general abstract simplicial complexes. As a result of this inv estigation, standard linear programming problems on these sets can be solved, including maximization of the Euler characteristics or of the sum of the Betti numbers.