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arXiv · 2105.09744

Squarefree powers of edge ideals of forests

Nursel Erey·Takayuki Hibi
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Abstract

Let $I(G)^{[k]}$ denote the $k$th squarefree power of the edge ideal of $G$. When $G$ is a forest, we provide a sharp upper bound for the regularity of $I(G)^{[k]}$ in terms of the $k$-admissable matching number of $G$. For any positive integer $k$, we classify all forests $G$ such that $I(G)^{[k]}$ has linear resolution. We also give a combinatorial formula for the regularity of $I(G)^{[2]}$ for any forest $G$.

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Nursel Erey, Takayuki Hibi. 2021-05-20. Squarefree powers of edge ideals of forests. https://doi.org/10.37236/10038

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