Abstract : 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.
https://hal.inria.fr/hal-01207560 Contributor : Coordination Episciences IamConnect in order to contact the contributor Submitted on : Thursday, October 1, 2015 - 9:28:26 AM Last modification on : Thursday, October 14, 2021 - 5:08:01 PM Long-term archiving on: : Saturday, January 2, 2016 - 10:39:53 AM
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⟩