A classification of the face numbers of Buchsbaum simplicial posets
Jonathan Browder, Steven Klee

TL;DR
This paper characterizes the face number vectors of Buchsbaum simplicial posets by proving that the known inequalities are both necessary and sufficient for given Betti numbers.
Contribution
It provides a complete characterization of the face vectors of Buchsbaum simplicial posets with specified Betti numbers, extending previous inequalities to sufficiency.
Findings
Necessary inequalities are also sufficient for face vectors.
Complete characterization of face numbers for Buchsbaum simplicial posets.
Extension of known results to prescribed Betti numbers.
Abstract
The family of Buchsbaum simplicial posets generalizes the family of simplicial cell manifolds. The -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 -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 -vectors of Buchsbaum simplicial posets with prescribed Betti numbers.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsTopological and Geometric Data Analysis · Commutative Algebra and Its Applications · Advanced Combinatorial Mathematics
