{"title":"线性代数中的结理论:Trip矩阵的一个例子","authors":"Molly A. Moran, Jessica Schenkman","doi":"10.1080/07468342.2023.2201163","DOIUrl":null,"url":null,"abstract":"Summary The trip matrix, introduced by Louis Zulli [6], gives a method for computing the Jones polynomial of a knot using basic Linear Algebra. We use this method to provide an alternative proof of the formula for the Jones polynomial of torus knots. In doing so, we provide a partial solution to an open question related to finding an elementary proof of the formula for general torus knots.","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"54 1","pages":"186 - 194"},"PeriodicalIF":0.0000,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Knot Theory in Linear Algebra: An Example with Trip Matrices\",\"authors\":\"Molly A. Moran, Jessica Schenkman\",\"doi\":\"10.1080/07468342.2023.2201163\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Summary The trip matrix, introduced by Louis Zulli [6], gives a method for computing the Jones polynomial of a knot using basic Linear Algebra. We use this method to provide an alternative proof of the formula for the Jones polynomial of torus knots. In doing so, we provide a partial solution to an open question related to finding an elementary proof of the formula for general torus knots.\",\"PeriodicalId\":38710,\"journal\":{\"name\":\"College Mathematics Journal\",\"volume\":\"54 1\",\"pages\":\"186 - 194\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"College Mathematics Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/07468342.2023.2201163\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Social Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"College Mathematics Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/07468342.2023.2201163","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Social Sciences","Score":null,"Total":0}
Knot Theory in Linear Algebra: An Example with Trip Matrices
Summary The trip matrix, introduced by Louis Zulli [6], gives a method for computing the Jones polynomial of a knot using basic Linear Algebra. We use this method to provide an alternative proof of the formula for the Jones polynomial of torus knots. In doing so, we provide a partial solution to an open question related to finding an elementary proof of the formula for general torus knots.
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