{"title":"The Rhodes semilattice of a biased graph","authors":"Michael J. Gottstein, Thomas Zaslavsky","doi":"10.1007/s00010-024-01039-3","DOIUrl":null,"url":null,"abstract":"<p>We reinterpret the Rhodes semilattices <span>\\(R_n({\\mathfrak {G}})\\)</span> of a group <span>\\({\\mathfrak {G}}\\)</span> in terms of gain graphs and generalize them to all gain graphs, both as sets of partition-potential pairs and as sets of subgraphs, and for the latter, further to biased graphs. Based on this we propose four different natural lattices in which the Rhodes semilattices and its generalizations are order ideals.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00010-024-01039-3","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
We reinterpret the Rhodes semilattices \(R_n({\mathfrak {G}})\) of a group \({\mathfrak {G}}\) in terms of gain graphs and generalize them to all gain graphs, both as sets of partition-potential pairs and as sets of subgraphs, and for the latter, further to biased graphs. Based on this we propose four different natural lattices in which the Rhodes semilattices and its generalizations are order ideals.
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
