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Ribbonlength of
families of folded ribbon knots
Elizabeth Denne, John Carr Haden, Troy Larsen and Emily Meehan
Vol. 15 (2022), No. 4, 591–628
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Abstract |
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We study Kauffman’s model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The folded ribbonlength is the length to width ratio of such a ribbon knot. We give upper bounds on the folded ribbonlength of 2-bridge, torus, twist, and pretzel knots, and these upper bounds turn out to be linear in the crossing number. We give a new way to fold torus knots and show that their folded ribbonlength is bounded above by . This means, for example, that the trefoil knot can be constructed with a folded ribbonlength of 6. We then show that any torus knot with has a constant , such that the folded ribbonlength is bounded above by . This provides an example of an upper bound on folded ribbonlength that is sublinear in crossing number. |
Keywords
knots, links, folded ribbon knots, ribbonlength, crossing
number, 2-bridge knots, torus knots, pretzel knots, twist
knots
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Mathematical Subject Classification
Primary: 57K10
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Milestones
Received: 9 November 2020
Revised: 23 July 2021
Accepted: 12 January 2022
Published: 7 January 2023
Communicated by Joel Foisy
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Authors |
| Elizabeth Denne | |
| Department of Mathematics Washington & Lee University Lexington, VA United States |
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| John Carr Haden | |
| Department of Mathematics Washington & Lee University Lexinton, VA United States |
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| Troy Larsen | |
| Department of Mathematics Washington & Lee University Lexington, VA United States |
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| Emily Meehan | |
| Department of Mathematics Wheaton College Norton, MA United States |
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