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arXiv · 2304.00255

Matchings, Squarefree Powers and Betti Splittings

Marilena Crupi·Antonino Ficarra·Ernesto Lax
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Abstract

Let $G$ be a finite simple graph and let $I(G)$ be its edge ideal. In this article, we deeply investigate the squarefree powers of $I(G)$ by means of Betti splittings. When $G$ is a forest, it is shown that the normalized depth function of $I(G)$ is non-increasing. Furthermore, we compute explicitly the regularity function of squarefree powers of $I(G)$ with $G$ a forest, confirming a conjecture of Erey and Hibi.

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Marilena Crupi, Antonino Ficarra, Ernesto Lax. 2023-04-01. Matchings, Squarefree Powers and Betti Splittings. https://arxiv.org/abs/2304.00255

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