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Edge ideals whose all matching powers are bi-Cohen-Macaulay

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arxiv 2503.08521 v2 pith:ALP32T5G submitted 2025-03-11 math.AC math.CO

Marilena Crupi , Antonino Ficarra This is my paper · ORCID
classification math.ACmath.CO
keywords matchingbi-cohen-macaulayedgepowersclassifygraphsidealideals
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abstract

We classify all graphs $G$ satisfying the property that all matching powers $I(G)^{[k]}$ of the edge ideal $I(G)$ are bi-Cohen-Macaulay for $1\le k\le\nu(G)$, where $\nu(G)$ is the maximum size of a matching of $G$.

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  1. Principal vector-spread Borel ideals

    math.AC 2025-07 conditional novelty 7.0 of 10

    For squarefree principal vector-spread Borel ideals, the paper gives the minimal primary decomposition, proves sequential Cohen-Macaulayness, and classifies normal torsionfreeness via the index bounds j_i <= sum_{s<=i} t_s.

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