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Combinatorial
random knots
Andrew Ducharme and Emily Peters |
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Vol. 13 (2020), No. 4, 633–654
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Abstract |
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We explore free knot diagrams, which are projections of knots into the plane which don’t record over/under data at crossings. We consider the combinatorial question of which free knot diagrams give which knots and with what probability. Every free knot diagram is proven to produce trefoil knots, and certain simple families of free knots are completely worked out. We make some conjectures (supported by computer-generated data) about bounds on the probability of a knot arising from a fixed free diagram being the unknot, trefoil, or figure-eight knot. |
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Keywords
knot theory, free knot diagrams, random knots,
combinatorics
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Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57M27
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Milestones
Received: 24 February 2020
Revised: 30 June 2020
Accepted: 7 July 2020
Published: 20 November 2020
Communicated by Kenneth S. Berenhaut
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Authors |
| Andrew Ducharme | |
| Department of Mathematics and
Statistics Loyola University Chicago Chicago, IL United States |
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| Emily Peters | |
| Department of Mathematics and
Statistics Loyola University Chicago Chicago, IL United States |
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| © 2020 MSP (Mathematical Sciences Publishers). |
