Matchings, Squarefree Powers and Betti Splittings

2023/04/01 by Marilena Crupı, Crupi, Marilena, Antonino Ficarra +3 · 2 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Commutative Algebra (math.AC) #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2304.00255

openalex publication_date 2023/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Admissible set and squarefree-power-like function with applications to squarefree symbolic powers
• Complementary edge ideals

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