Monomial ideals whose all matching powers are Cohen-Macaulay

2024/10/02 by Antonino Ficarra, Ficarra, Antonino, Somayeh Moradi +1 · 1 citation
Computer Science · Mathematics · #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2410.01666

openalex publication_date 2024/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In the present paper, we aim to classify monomial ideals whose all matching powers are Cohen-Macaulay. We especially focus our attention on edge ideals. The Cohen-Macaulayness of the last matching power of an edge ideal is characterized, providing an algebraic analogue of the famous Tutte theorem regarding graphs having a perfect matching. For chordal graphs, very well-covered graphs and Cameron-Walker graphs, we completely solve our problem.

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

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