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

f-vectors of Simplicial Posets that are Balls