Vol. 15, No. 2, 2022

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Petal projections, knot colorings and determinants

Allison Henrich and Robin Truax

Vol. 15 (2022), No. 2, 207–232

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 p-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 10 from their petal permutations.

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petal projection, knot determinant, colorability
Mathematical Subject Classification
Primary: 57K10
Supplementary material


Received: 31 March 2020
Revised: 13 August 2021
Accepted: 9 October 2021
Published: 29 July 2022

Communicated by Kenneth S. Berenhaut
Allison Henrich
Department of Mathematics
Seattle University
Seattle, WA
United States
Robin Truax
Department of Mathematics
Stanford University
Stanford, CA
United States