{"title":"Comparison of symbolic and ordinary powers of parity binomial edge ideals","authors":"Nadia Taghipour, Shamila Bayati, Farhad Rahmati","doi":"10.1007/s00605-023-01912-4","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate when symbolic and ordinary powers of the parity binomial edge ideal of a graph fail to be equal. It turns out that if $${\\mathcal {I}}_{G}$$ is the parity binomial edge ideal of a graph G, then in each of the following cases the symbolic power $${\\mathcal {I}}_{G}^{(t)}$$ and the ordinary power $${\\mathcal {I}}_{G}^t$$ are not equal for some t: (i) the clique number of G is greater than 3; (ii) G has a net; or (iii) G has a PT as an induced subgraph.","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-023-01912-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate when symbolic and ordinary powers of the parity binomial edge ideal of a graph fail to be equal. It turns out that if $${\mathcal {I}}_{G}$$ is the parity binomial edge ideal of a graph G, then in each of the following cases the symbolic power $${\mathcal {I}}_{G}^{(t)}$$ and the ordinary power $${\mathcal {I}}_{G}^t$$ are not equal for some t: (i) the clique number of G is greater than 3; (ii) G has a net; or (iii) G has a PT as an induced subgraph.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
