## Browder, Jonathan and Klee, Steven - Bucshbaum simplicial posets

dmtcs:2452 - Discrete Mathematics & Theoretical Computer Science, January 1, 2014, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Bucshbaum simplicial posets

Authors: Browder, Jonathan and Klee, Steven

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.

Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)
Section: Proceedings
Published on: January 1, 2014
Submitted on: November 21, 2016
Keywords: Simplicial complex,simplicial poset,f-vector,h-vector,Cohen-Macaulay,Buchsbaum,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]