f-vectors of Simplicial Posets that are Balls

Abstract

Results of R. Stanley and M. Masuda completely characterize the h-vectors of simplicial posets whose order complexes are spheres. In this paper we examine the corresponding question in the case where the order complex is a ball. Using the face rings of these posets, we develop a series of new conditions on their h-vectors. We also present new methods for constructing poset balls with specific h-vectors. These results allow us to give a complete characterization of the h-vectors of simplicial poset balls up through dimension six.