{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:30:30Z","timestamp":1772253030764,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,7]],"date-time":"2018-11-07T00:00:00Z","timestamp":1541548800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS1519375 and DMS1716987"],"award-info":[{"award-number":["DMS1519375 and DMS1716987"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Proper identification of oriented knots and 2-component links requires a precise link nomenclature. Motivated by questions arising in DNA topology, this study aims to produce a nomenclature unambiguous with respect to link symmetries. For knots, this involves distinguishing a knot type from its mirror image. In the case of 2-component links, there are up to sixteen possible symmetry types for each link type. The study revisits the methods previously used to disambiguate chiral knots and extends them to oriented 2-component links with up to nine crossings. Monte Carlo simulations are used to report on writhe, a geometric indicator of chirality. There are ninety-two prime 2-component links with up to nine crossings. Guided by geometrical data, linking number, and the symmetry groups of 2-component links, canonical link diagrams for all but five link types (9 5 2,     9 34 2,     9 35 2,     9 39 2, and     9 41 2) are proposed. We include complete tables for prime knots with up to ten crossings and prime links with up to nine crossings. We also prove a result on the behavior of the writhe under local lattice moves.<\/jats:p>","DOI":"10.3390\/sym10110604","type":"journal-article","created":{"date-parts":[[2018,11,7]],"date-time":"2018-11-07T10:32:07Z","timestamp":1541586727000},"page":"604","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Symmetry Motivated Link Table"],"prefix":"10.3390","volume":"10","author":[{"given":"Shawn","family":"Witte","sequence":"first","affiliation":[{"name":"Department of Mathematics, One Shields Ave., University of California, Davis, CA 95616, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michelle","family":"Flanner","sequence":"additional","affiliation":[{"name":"Department of Microbiology &amp; Molecular Genetics, One Shields Ave., University of California, Davis, CA 95616, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8328-6806","authenticated-orcid":false,"given":"Mariel","family":"Vazquez","sequence":"additional","affiliation":[{"name":"Department of Mathematics, One Shields Ave., University of California, Davis, CA 95616, USA"},{"name":"Department of Microbiology &amp; Molecular Genetics, One Shields Ave., University of California, Davis, CA 95616, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,7]]},"reference":[{"key":"ref_1","first-page":"562","article-title":"On types of knotted curves","volume":"28","author":"Briggs","year":"1927","journal-title":"Ann. 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