Regularity of powers of path ideals of line graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909219945447424 |
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| author | Shan, Jiawen Lu, Dancheng |
| author_facet | Shan, Jiawen Lu, Dancheng |
| contents | Let $L_n$ be a line graph with $n$ vertices and let $I$ be its $t$-path ideal. It is shown that $I^s$ has a linear resolution for some $s\geq 1$ (or equivalently for all $s\geq 1$) if and only if $I^s$ has linear quotients for some $s\geq 1$ (or equivalently for all $s\geq 1$) if and only if $t\leq n\leq 2t$. In addition, we present an explicit formula for the regularity of $I^s$ for all $s\geq 1$. It turns out it is linear in $s$ from the very beginning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00670 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regularity of powers of path ideals of line graphs Shan, Jiawen Lu, Dancheng Commutative Algebra Primary 13A02, 05E40, Secondary 06D50 Let $L_n$ be a line graph with $n$ vertices and let $I$ be its $t$-path ideal. It is shown that $I^s$ has a linear resolution for some $s\geq 1$ (or equivalently for all $s\geq 1$) if and only if $I^s$ has linear quotients for some $s\geq 1$ (or equivalently for all $s\geq 1$) if and only if $t\leq n\leq 2t$. In addition, we present an explicit formula for the regularity of $I^s$ for all $s\geq 1$. It turns out it is linear in $s$ from the very beginning. |
| title | Regularity of powers of path ideals of line graphs |
| topic | Commutative Algebra Primary 13A02, 05E40, Secondary 06D50 |
| url | https://arxiv.org/abs/2305.00670 |