Depth and regularity of powers of edge ideals of edge-weighted trees
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912580652498944 |
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| author | Hien, Truong Thi Li, Jiaxin Trung, Tran Nam Zhu, Guangjun |
| author_facet | Hien, Truong Thi Li, Jiaxin Trung, Tran Nam Zhu, Guangjun |
| contents | For an increasing weighted tree $G_ω$, we obtain an asymptotic value and a sharp bound on the index stability of the depth function of its edge ideal $I(G_ω)$. Moreover, if $G_ω$ is a strictly increasing weighted tree, we provide the minimal free resolution of $I(G_ω)$ and an exact formula for the regularity of all powers of $I(G_ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Depth and regularity of powers of edge ideals of edge-weighted trees Hien, Truong Thi Li, Jiaxin Trung, Tran Nam Zhu, Guangjun Commutative Algebra Primary 13C15, 13C10, Secondary 05E40, 05C05 For an increasing weighted tree $G_ω$, we obtain an asymptotic value and a sharp bound on the index stability of the depth function of its edge ideal $I(G_ω)$. Moreover, if $G_ω$ is a strictly increasing weighted tree, we provide the minimal free resolution of $I(G_ω)$ and an exact formula for the regularity of all powers of $I(G_ω)$. |
| title | Depth and regularity of powers of edge ideals of edge-weighted trees |
| topic | Commutative Algebra Primary 13C15, 13C10, Secondary 05E40, 05C05 |
| url | https://arxiv.org/abs/2509.08688 |