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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
Appendices
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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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