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Linear upper bounds on
ribbonlength of knots and links
Hyoungjun Kim, Sungjong No and Hyungkee Yoo |
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Algebraic & Geometric Topology 26 (2026) 553–563
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Abstract |
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A knotted ribbon is one physical aspect of a knot. A folded ribbon knot is a depiction of a knot obtained by folding a long and thin rectangular strip to become flat. The ribbonlength of a knot type can be defined as the minimum length required to tie the given knot type as a folded ribbon knot. The ribbonlength has been conjectured to grow linearly or sublinearly with respect to a minimal crossing number. Several knot types provide evidence that this conjecture is true, but there is no proof for general cases. In this paper, we show that for any knot or link, the ribbonlength is bounded by a linear function of the crossing number. In more detail, for a knot or link . Our approach involves binary grid diagrams and bisected vertex leveling techniques. |
Keywords
ribbonlength, folded ribbon knot
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Mathematical Subject Classification
Primary: 57K10
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References |
Publication
Received: 19 March 2024
Revised: 16 December 2024
Accepted: 22 March 2025
Published: 11 February 2026
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Authors |
| Hyoungjun Kim | |
| Department of Mathematics
Education Kyungpook National University Daegu South Korea |
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| Sungjong No | |
| Department of Mathematics Kyonggi University Suwon South Korea |
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| Hyungkee Yoo | |
| Department of Mathematics
Education Sunchon National University Suncheon South Korea |
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| © 2026 MSP (Mathematical Sciences Publishers). |
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