结表多达五个三重交叉和移动之间的定向图

IF 0.4 4区数学 Q4 MATHEMATICS

Tokyo Journal of Mathematics Pub Date : 2023-06-01 DOI:10.3836/tjm/1502179382

Michał Jabłonowski

{"title":"结表多达五个三重交叉和移动之间的定向图","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":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"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\":null,\"pages\":null},\"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}","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

摘要

我们列举并显示最小图表，所有素数结，直到三交数等于5。我们导出了连接同一方向结的三交叉图的方向移动的最小生成集。我们还提出了一个关于结的三交数的严格下界与其亚历山大多项式的宽度有关的猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Tabulation of Knots Up to Five Triple-crossings and Moves between Oriented Diagrams

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Tokyo Journal of Mathematics MATHEMATICS-

CiteScore

0.70

自引率

16.70%

发文量

审稿时长

>12 weeks

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.