f-vectors and h-vectors of simplicial posets

AbstractA simplicial poset is a (finite) poset P with Ô such that every interval [Ô, x] is a boolean algebra. Simplicial posets are generalizations of simplicial complexes. The f-vector f(P) = (f0, f1,…, fd−1) of a simplicial poset P of rank d is defined by fi=♯{xεP: [Ô,x]≊Bi+1}, where Bi+1 is a boolean algebra of rank i+1. We give a complete characterization of the f-vectors of simplicial posets and of Cohen-Macaulay simplicial posets, and an almost complete characterization for Gorenstein simplicial posets. The Cohen-Macaulay case relies on the theory of algebras with straightening laws (ASL's)