Matchings, Squarefree Powers and Betti Splittings
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917618669060096 |
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| author | Crupi, Marilena Ficarra, Antonino Lax, Ernesto |
| author_facet | Crupi, Marilena Ficarra, Antonino Lax, Ernesto |
| contents | Let $G$ be a finite simple graph and let $I(G)$ be its edge ideal. In this article, we deeply investigate the squarefree powers of $I(G)$ by means of Betti splittings. When $G$ is a forest, it is shown that the normalized depth function of $I(G)$ is non-increasing. Furthermore, we compute explicitly the regularity function of squarefree powers of $I(G)$ with $G$ a forest, confirming a conjecture of Erey and Hibi. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00255 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Matchings, Squarefree Powers and Betti Splittings Crupi, Marilena Ficarra, Antonino Lax, Ernesto Commutative Algebra Let $G$ be a finite simple graph and let $I(G)$ be its edge ideal. In this article, we deeply investigate the squarefree powers of $I(G)$ by means of Betti splittings. When $G$ is a forest, it is shown that the normalized depth function of $I(G)$ is non-increasing. Furthermore, we compute explicitly the regularity function of squarefree powers of $I(G)$ with $G$ a forest, confirming a conjecture of Erey and Hibi. |
| title | Matchings, Squarefree Powers and Betti Splittings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2304.00255 |