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arXiv · 2410.01666

Monomial ideals whose all matching powers are Cohen-Macaulay

Antonino Ficarra·Somayeh Moradi
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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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Antonino Ficarra, Somayeh Moradi. 2024-10-02. Monomial ideals whose all matching powers are Cohen-Macaulay. https://arxiv.org/abs/2410.01666

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