2013/07/05 by Jonathan Browder, Browder, Jonathan, Steven Klee +1
Computer Science · Mathematics · #05E #06A07 #52B05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis #math.CO #msc:05E #msc:06A07 #msc:52B05
paper · pdf · doi:10.48550/arxiv.1307.1548
16 pages. Updated; added section 5 (on manifolds)
openalex publication_date 2013/07/05 · arxiv created 2013/10/05 · arxiv updated 2013/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.