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. Combining this work with a new result of S. Murai we are able to give a complete characterization of the h-vectors of simplicial poset balls in all even dimensions, as well as odd dimensions less than or equal to five.
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