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The mathematics
of tie knots
Elizabeth Denne, Corinne Joireman and Allison Young
Vol. 14 (2021), No. 2, 241–270
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Abstract |
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In 2000, Thomas Fink and Yong Mao studied neck ties and, with certain assumptions, found 85 different ways to tie a neck tie. They gave a formal language which describes how a tie is made, giving a sequence of moves for each neck tie. The ends of a neck tie can be joined together, which gives a physical model of a mathematical knot that we call a tie knot. In this paper we classify the knot type of each of Fink and Mao’s 85 tie knots. We describe how the unknot, left and right trefoil, twist knots and torus knots can be recognized from their sequence of moves. We also view tie knots as a family within the set of all knots. Among other results, we prove that any tie knot is prime and alternating. |
Keywords
knots, neck ties, torus knot, twist knot, alternating knot,
prime knot
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Mathematical Subject Classification
Primary: 57K10
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Milestones
Received: 28 May 2020
Revised: 30 October 2020
Accepted: 25 November 2020
Published: 6 April 2021
Communicated by Colin Adams
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Authors |
| Elizabeth Denne | |
| Department of Mathematics Washington & Lee University Lexington, VA United States |
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| Corinne Joireman | |
| Washington & Lee
University Lexington, VA United States |
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| Allison Young | |
| University of Virginia Charlottesville, VA United States |
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