Matchings, Squarefree Powers and Betti Splittings

arXiv2304.00255MaRDI QIDQ6509453

Antonino Ficarra, Author name not available (Why is that?), Marilena Crupi

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. Finally, we introduce the strong squarefree Ratliff property, and prove that all squarefree monomial ideals satisfy such a property.

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