{"title":"Proof of a Conjecture of Proctor and Scoppetta Related to d-Complete Posets","authors":"J. Farley","doi":"10.1556/314.2022.00009","DOIUrl":null,"url":null,"abstract":"Proctor and Scoppetta conjectured that\n \n \n \n (1) there exists an infinite locally finite poset that satisfies their conditions VT and NTC but not SIS;\n \n \n (2) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MF but not both VT and FT; and\n \n \n (3) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MD but not NCC.\n \n \n \n In this note, the conjecture of Proctor and Scoppetta, which is related to d-complete posets, is proven.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"143 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Pannonica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1556/314.2022.00009","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
Proctor and Scoppetta conjectured that
(1) there exists an infinite locally finite poset that satisfies their conditions VT and NTC but not SIS;
(2) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MF but not both VT and FT; and
(3) there exists an infinite locally finite poset satisfying their conditions D3-C and D3MD but not NCC.
In this note, the conjecture of Proctor and Scoppetta, which is related to d-complete posets, is proven.
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