{"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}
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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.
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