{"title":"Tabulation of Knots Up to Five Triple-crossings and Moves between Oriented Diagrams","authors":"Michał Jabłonowski","doi":"10.3836/tjm/1502179382","DOIUrl":null,"url":null,"abstract":"We enumerate and show tables of minimal diagrams for all prime knots up to the triple-crossing number equal to five. We derive a minimal generating set of oriented moves connecting triple-crossing diagrams of the same oriented knot. We also present a conjecture about a strict lower bound of the triple-crossing number of a knot related to the breadth of its Alexander polynomial.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.4000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tokyo Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3836/tjm/1502179382","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
We enumerate and show tables of minimal diagrams for all prime knots up to the triple-crossing number equal to five. We derive a minimal generating set of oriented moves connecting triple-crossing diagrams of the same oriented knot. We also present a conjecture about a strict lower bound of the triple-crossing number of a knot related to the breadth of its Alexander polynomial.
期刊介绍：
The Tokyo Journal of Mathematics was founded in 1978 with the financial support of six institutions in the Tokyo area: Gakushuin University, Keio University, Sophia University, Tokyo Metropolitan University, Tsuda College, and Waseda University. In 2000 Chuo University and Meiji University, in 2005 Tokai University, and in 2013 Tokyo University of Science, joined as supporting institutions.
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