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 $\mathrm{Spec}R$. Further, we show that $R$ is almost Gorenstein. Moreover, we show that the conjecture of Hibi and Tsuchiya is true.

arXiv commentarXiv admin note: text overlap with arXiv:2201.02957, arXiv:2005.03259