Graded Betti numbers of powers of path ideals of paths
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929337634127872 |
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| author | Balanescu, Silviu Cimpoeas, Mircea Vu, Thanh |
| author_facet | Balanescu, Silviu Cimpoeas, Mircea Vu, Thanh |
| contents | Let $I_{n,m} = (x_1\cdots x_{m},x_2 \cdots x_{m+1},\ldots,x_{n+1}x_{n+2}\cdots x_{n+m})$ be the $m$-path ideal of a path of length $n + m-1$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_{n+m}]$. We compute all the graded Betti numbers of all powers of $I_{n,m}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graded Betti numbers of powers of path ideals of paths Balanescu, Silviu Cimpoeas, Mircea Vu, Thanh Commutative Algebra 13D02 Let $I_{n,m} = (x_1\cdots x_{m},x_2 \cdots x_{m+1},\ldots,x_{n+1}x_{n+2}\cdots x_{n+m})$ be the $m$-path ideal of a path of length $n + m-1$ over a polynomial ring $S = \mathrm{k}[x_1,\ldots,x_{n+m}]$. We compute all the graded Betti numbers of all powers of $I_{n,m}$. |
| title | Graded Betti numbers of powers of path ideals of paths |
| topic | Commutative Algebra 13D02 |
| url | https://arxiv.org/abs/2405.04747 |