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arXiv · 2305.00670

Regularity of powers of path ideals of line graphs

Jiawen Shan·Dancheng Lu
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Abstract

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.

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Jiawen Shan, Dancheng Lu. 2023-05-01. Regularity of powers of path ideals of line graphs. https://arxiv.org/abs/2305.00670

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