Betti numbers of weighted oriented graphs
| Autor: | Beata Casiday, Selvi Kara |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mapping cone (topology)
Mathematics::Commutative Algebra Betti number Applied Mathematics Dimension (graph theory) Structure (category theory) Commutative Algebra (math.AC) Mathematics - Commutative Algebra Graph Theoretical Computer Science Combinatorics Computational Theory and Mathematics 13D02 13F20 05C25 05C75 FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics Geometry and Topology Ideal (ring theory) Combinatorics (math.CO) Mathematics |
| Popis: | Let $\mathcal{D}$ be a weighted oriented graph and $I(\mathcal{D})$ be its edge ideal. In this paper, we investigate the Betti numbers of $I(\mathcal{D})$ via upper-Koszul simplicial complexes, Betti splittings and the mapping cone construction. In particular, we provide recursive formulas for the Betti numbers of edge ideals of several classes of weighted oriented graphs. We also identify classes of weighted oriented graphs whose edge ideals have a unique extremal Betti number which allows us to compute the regularity and projective dimension for the identified classes. Furthermore, we characterize the structure of a weighted oriented graph $\mathcal{D}$ on $n$ vertices such that $\textrm{pdim } (R/I(\mathcal{D}))=n$ where $R=k[x_1,\ldots, x_n]$. 16 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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