On $f$- and $h$-vectors of relative simplicial complexes
| Autor: | Lukas Katthän, Raman Sanyal, Giulia Codenotti |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
05E45 (Primary) 05E40
13F55 (Secondary) Mathematics::Commutative Algebra Polynomial ring 010102 general mathematics Structure (category theory) Of the form 0102 computer and information sciences Characterization (mathematics) Commutative Algebra (math.AC) Mathematics - Commutative Algebra 01 natural sciences Combinatorics Topological combinatorics Simplicial complex 010201 computation theory & mathematics FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) 0101 mathematics Algebraic number Quotient Mathematics |
| Zdroj: | Algebraic Combinatorics. 2:343-353 |
| ISSN: | 2589-5486 |
| DOI: | 10.5802/alco.38 |
| Popis: | A relative simplicial complex is a collection of sets of the form $\Delta \setminus \Gamma$, where $\Gamma \subset \Delta$ are simplicial complexes. Relative complexes played key roles in recent advances in algebraic, geometric, and topological combinatorics but, in contrast to simplicial complexes, little is known about their general combinatorial structure. In this paper, we address a basic question in this direction and give a characterization of $f$-vectors of relative (multi)complexes on a ground set of fixed size. On the algebraic side, this yields a characterization of Hilbert functions of quotients of homogeneous ideals over polynomial rings with a fixed number of indeterminates. Moreover, we characterize $h$-vectors of fully Cohen--Macaulay relative complexes as well as $h$-vectors of Cohen--Macaulay relative complexes with minimal faces of given dimensions. The latter resolves a question of Bj\"orner. Comment: accepted for publication in Algebraic Combinatorics |
| Databáze: | OpenAIRE |
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