  The family of Buchsbaum simplicial posets generalizes the family of
simplicial cell manifolds. The $h'$-vector of a simplicial complex or
simplicial poset encodes the combinatorial and topological data of its face
numbers and the reduced Betti numbers of its geometric realization. Novik and
Swartz showed that the $h'$-vector of a Buchsbaum simplicial poset satisfies
certain simple inequalities; in this paper we show that these necessary
conditions are in fact sufficient to characterize the $h'$-vectors of Buchsbaum
simplicial posets with prescribed Betti numbers.

Combinatorics