TL;DR
This paper establishes a precise characterization linking the Cohen-Macaulay property of all symbolic powers of Stanley-Reisner ideals to the matroid structure of the associated simplicial complex.
Contribution
It proves that the symbolic powers are Cohen-Macaulay if and only if the simplicial complex is a matroid, providing a complete characterization.
Findings
All symbolic powers are Cohen-Macaulay iff the complex is a matroid
Characterization of Cohen-Macaulay symbolic powers in combinatorial terms
Bridges algebraic properties with combinatorial structures
Abstract
We prove that all the symbolic powers of a Stanley-Reisner ideal are Cohen-Macaulay if and only if the associated simplicial complex is a matroid.
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