Aysan Behnia, Gholam Hossein Fath-Tabar, Gyula O. H. Katona
{"title":"Forbidden Subposets in the Cycle Poset","authors":"Aysan Behnia, Gholam Hossein Fath-Tabar, Gyula O. H. Katona","doi":"10.1007/s11083-024-09673-x","DOIUrl":null,"url":null,"abstract":"<p>The cycle poset consists of the intervals of the cyclic permutation of the elements <b>1, 2, ...</b>, <i>n</i>, ordered by inclusion. Suppose that <b><i>F</i></b> is a set of such intervals, none of them is a less than <b><i>s</i></b> others. The maximum size of <b><i>F</i></b> is determined under this condition. It is also shown that if the largest size of a set in this poset without containing a small subposet <b><i>P</i></b> is known, it solves the same problem, up to an additive constant, in the grid poset consisting of the pairs <span>\\((i,j) (1\\le i,j\\le n)\\)</span> and ordered coordinate-wise.</p>","PeriodicalId":501237,"journal":{"name":"Order","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Order","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11083-024-09673-x","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
The cycle poset consists of the intervals of the cyclic permutation of the elements 1, 2, ..., n, ordered by inclusion. Suppose that F is a set of such intervals, none of them is a less than s others. The maximum size of F is determined under this condition. It is also shown that if the largest size of a set in this poset without containing a small subposet P is known, it solves the same problem, up to an additive constant, in the grid poset consisting of the pairs \((i,j) (1\le i,j\le n)\) and ordered coordinate-wise.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
