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Matchings, Squarefree Powers and Betti Splittings
Published 1 Apr 2023 in math.AC | (2304.00255v3)
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.
- Ficarra, A.: Matching Powers: Macaulay2 Package. Preprint at https://arxiv.org/abs/2312.13007 (2023)
- Seyed Fakhari S. A.: On the Castelnuovo-Mumford regularity of squarefree powers of edge ideals. J. Pure Appl. Algebra 228(3) (2024) https://doi.org/10.1016/j.jpaa.2023.107488
- Seyed Fakhari, S. A.: On the Regularity of squarefree part of symbolic powers of edge ideals. Preprint at https://arxiv.org/abs/2303.02791 (2023)
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