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Petal
projections, knot colorings and determinants
Allison Henrich and Robin Truax
Vol. 15 (2022), No. 2, 207–232
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Abstract |
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An übercrossing diagram is a knot diagram with only one crossing that may involve more than two strands of the knot. Such a diagram without any nested loops is called a petal projection. Every knot has a petal projection from which the knot can be recovered using a permutation that represents strand heights. Using this permutation, we give an algorithm that determines the -colorability and the determinants of knots from their petal projections. In particular, we compute the determinants of all prime knots with crossing number less than from their petal permutations. |
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Keywords
petal projection, knot determinant, colorability
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Mathematical Subject Classification
Primary: 57K10
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Supplementary material |
Milestones
Received: 31 March 2020
Revised: 13 August 2021
Accepted: 9 October 2021
Published: 29 July 2022
Communicated by Kenneth S. Berenhaut
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Authors |
| Allison Henrich | |
| Department of Mathematics Seattle University Seattle, WA United States |
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| Robin Truax | |
| Department of Mathematics Stanford University Stanford, CA United States |
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