{"title":"A Characterization of Sequentially Cohen–Macaulay Matroidal Ideals","authors":"Payman Mahmood Hamaali, A. Mafi, H. Saremi","doi":"10.1142/s1005386723000196","DOIUrl":null,"url":null,"abstract":"Let [Formula: see text] be the polynomial ring in [Formula: see text] variables over a field [Formula: see text] and [Formula: see text] be a matroidal ideal of [Formula: see text]. We show that [Formula: see text] is sequentially Cohen–Macaulay if and only if the [Formula: see text] has linear quotients. As a consequence, [Formula: see text] is sequentially Cohen–Macaulay if and only if [Formula: see text] is shellable.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s1005386723000196","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Let [Formula: see text] be the polynomial ring in [Formula: see text] variables over a field [Formula: see text] and [Formula: see text] be a matroidal ideal of [Formula: see text]. We show that [Formula: see text] is sequentially Cohen–Macaulay if and only if the [Formula: see text] has linear quotients. As a consequence, [Formula: see text] is sequentially Cohen–Macaulay if and only if [Formula: see text] is shellable.
设[公式:见文]为[公式:见文]域中变量[公式:见文]中的多项式环，[公式:见文]为[公式:见文]的矩阵理想。我们证明，当且仅当[公式:见文本]具有线性商时，[公式:见文本]是顺序Cohen-Macaulay。因此，当且仅当[Formula: see text]是可shell时，[Formula: see text]是顺序Cohen-Macaulay。
分享
京公网安备 11010802042870号
京ICP备2023020795号-1
求助内容：
应助结果提醒方式：
扫码关注我们
