{"title":"Non-Gorenstein Locus and Almost Gorenstein Property of the Ehrhart Ring of the Stable Set Polytope of a Cycle Graph","authors":"Mitsuhiro Miyazaki","doi":"10.11650/tjm/221104","DOIUrl":null,"url":null,"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.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.11650/tjm/221104","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
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.
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