{"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":22176,"journal":{"name":"Taiwanese Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Taiwanese Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.11650/tjm/221104","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","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.
期刊介绍：
The Taiwanese Journal of Mathematics, published by the Mathematical Society of the Republic of China (Taiwan), is a continuation of the former Chinese Journal of Mathematics (1973-1996). It aims to publish original research papers and survey articles in all areas of mathematics. It will also occasionally publish proceedings of conferences co-organized by the Society. The purpose is to reflect the progress of the mathematical research in Taiwan and, by providing an international forum, to stimulate its further developments. The journal appears bimonthly each year beginning from 2008.
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