Algebraic study on permutation graphs

Published 27 Feb 2025 in math.AC and math.CO | (2502.19992v1)

Abstract: Let $G$ be a permutation graph. We show that $G$ is Cohen-Macaulay if and only if $G$ is unmixed and vertex decomposable. When this is the case, we obtain a combinatorial description for the $a$-invariant of $G$. Moreover, we characterize the Gorenstein permutation graphs.

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