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2021 The mathematics of tie knots
Elizabeth Denne, Corinne Joireman, Allison Young
Involve 14(2): 241-270 (2021). DOI: 10.2140/involve.2021.14.241

Abstract

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 (2,p) 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.

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Elizabeth Denne. Corinne Joireman. Allison Young. "The mathematics of tie knots." Involve 14 (2) 241 - 270, 2021. https://doi.org/10.2140/involve.2021.14.241

Information

Received: 28 May 2020; Revised: 30 October 2020; Accepted: 25 November 2020; Published: 2021
First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/involve.2021.14.241

Subjects:
Primary: 57K10

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 2 • 2021
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