{"title":"A Proof of the Alternate Thomassé Conjecture for Countable N-Free Posets","authors":"Davoud Abdi","doi":"10.1007/s11083-023-09650-w","DOIUrl":null,"url":null,"abstract":"<p>An <i>N</i>-free poset is a poset whose comparability graph does not embed an induced path with four vertices. We use the well-quasi-order property of the class of countable <i>N</i>-free posets and some labelled ordered trees to show that a countable <i>N</i>-free poset has one or infinitely many siblings, up to isomorphism. This, partially proves a conjecture stated by Thomassé for this class.</p>","PeriodicalId":501237,"journal":{"name":"Order","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-11-20","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/s11083-023-09650-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
An N-free poset is a poset whose comparability graph does not embed an induced path with four vertices. We use the well-quasi-order property of the class of countable N-free posets and some labelled ordered trees to show that a countable N-free poset has one or infinitely many siblings, up to isomorphism. This, partially proves a conjecture stated by Thomassé for this class.
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