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Open AccessArticle

A Symmetry Motivated Link Table

1
Department of Mathematics, One Shields Ave., University of California, Davis, CA 95616, USA
2
Department of Microbiology & Molecular Genetics, One Shields Ave., University of California, Davis, CA 95616, USA
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(11), 604; https://doi.org/10.3390/sym10110604
Received: 14 August 2018 / Revised: 20 October 2018 / Accepted: 22 October 2018 / Published: 7 November 2018
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. View Full-Text
Keywords: writhe; chirality; nomenclature; link symmetries; link table; knot table; lattice polygons; DNA topology writhe; chirality; nomenclature; link symmetries; link table; knot table; lattice polygons; DNA topology
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Witte, S.; Flanner, M.; Vazquez, M. A Symmetry Motivated Link Table. Symmetry 2018, 10, 604.

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