The first 1,701,936 knots

  title={The first 1,701,936 knots},
  author={Jimmy-John O. E. Hoste and Morwen Thistlethwaite and Jeffrey R. Weeks},
  journal={The Mathematical Intelligencer},
inc lude all pr ime knots wi th 16 or fewer crossings. This r epresen t s more than a 130-fold increase in the number of t abu la ted knots s ince the last burs t of tabula t ion tha t t ook p lace in the early 1980s. With more than 1.7 mil l ion knots now in the tables, we hope that the census will serve as a r ich source of examples and coun te rexamples and as a genera l test ing ground for our collective intuition. To this end, we have wri t ten a UNIX-based compute r p rog ram cal led… 

The 250 Knots with up to 10 Crossings

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The “Perko pair” knot 10161 = 10162 [R, p. 415; identification noted in second printing] is exceptional in at least two distinct ways. It first achieved its name and fame when Perko [P] discovered

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  • C. Adams
  • Mathematics
    The Mathematical Intelligencer
  • 2021
J ohn Conway’s impact has been felt far across mathematics. His interests were wide, and through his often playful approach, he uncovered fundamental theories that allowed for whole areas of research

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We give a brief historical overview of the Tait conjectures, made 120 years ago in the course of his pioneering work in tabulating the simplest knots, and solved a century later using the Jones

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At its core, this thesis is a study of knots, objects which human beings encounter with extraordinary frequency. We may find them on our person (in our shoelaces and neckties), or around our homes

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T ake a length of rope, loop and weave it around itself and connect its ends. The result , of course, is a knot. Creating a knot seems simple, yet knot theory is one of the most active fields in

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IX.—Alternate ± Knots of Order Eleven

  • C. N. Little
  • Mathematics
    Transactions of the Royal Society of Edinburgh
  • 1892
1. A year ago last April, Prof. Tait proposed that I should undertake to derive from Mr Kirkman's polyhedral drawings the alternate ± knots of eleven crossings, thus doing for order 11 what had been

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Linking numbers between branch curves of irregular covering spaces of knots are used to extend the classification of knots through ten crossings and to show that the only amphicheirals in

XXVI.—The 364 Unifilar Knots of Ten Crossings, Enumerated and Described

  • T. Kirkman
  • History
    Transactions of the Royal Society of Edinburgh
  • 1886
The 119 subsolids (marked ss) and the 244 unsolids (marked us), of these unifilars are here arranged in lists according to their flaps. Fe is the number of flaps of e loops upon a knot; and the

XXX.—Non-Alternate ± Knots

  • C. N. Little
  • Mathematics
    Transactions of the Royal Society of Edinburgh
  • 1900
1. The following paper is a contribution to the theory of non-alternate ± knots, together with a census of these knots for Order Ten; that is, all the knots are given which have in reduced form just

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  • T. Kirkman
  • Art
    Transactions of the Royal Society of Edinburgh
  • 1884
1. By a knot of n crossings, I understand a reticulation of any number of meshes of two or more edges, whose summits, all tessaraces (ἀκή), are each a single crossing, as when you cross your

XVIII.—Non-Alternate ± Knots, of Orders Eight and Nine

  • C. N. Little
  • Mathematics
    Transactions of the Royal Society of Edinburgh
  • 1890
1. To complete the census of knots of any given order, that is, minimum number of crossings, it is necessary to include not only those in which the crossings are taken alternately over and under