Non-Gorenstein Locus and Almost Gorenstein Property of the Ehrhart Ring of the Stable Set Polytope of a Cycle Graph

Abstract

Let $R$ be the Ehrhart ring of the stable set polytope of a cycle graph which is not Gorenstein. We describe the non-Gorenstein locus of $\operatorname{Spec}R$. Further, we show that $R$ is almost Gorenstein. Moreover, we show that the conjecture of Hibi and Tsuchiya is true.