Bucshbaum simplicial posets

Jonathan Browder (1) , Steven Klee (2)

1 Department of Mathematics [Aalto]
2 Department of Mathematics [Seattle University]

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.

Mots clés: simplicial poset; f-vector; h-vector; Cohen-Macaulay; Buchsbaum; Simplicial complex

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Jonathan Browder, Steven Klee. Bucshbaum simplicial posets. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.911-922, ⟨10.46298/dmtcs.2452⟩. ⟨hal-01207560⟩