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
Abstract

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.

Keywords
petal projection, knot determinant, colorability
Mathematical Subject Classification
Primary: 57K10
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Received: 31 March 2020
Revised: 13 August 2021
Accepted: 9 October 2021
Published: 29 July 2022

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