https://hal.inria.fr/hal-01207560Browder, JonathanJonathanBrowderDepartment of Mathematics [Aalto] - Aalto UniversityKlee, StevenStevenKleeDepartment of Mathematics [Seattle University] - Seattle University [Seattle]Bucshbaum simplicial posetsHAL CCSD2014simplicial posetf-vectorh-vectorCohen-MacaulayBuchsbaumSimplicial complex[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]Episciences Iam, CoordinationLouis J. Billera and Isabella Novik2015-10-01 09:28:262021-10-14 17:08:012015-10-01 09:32:41enConference papershttps://hal.inria.fr/hal-01207560/document10.46298/dmtcs.2452application/pdf1The 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.