Petal Projections, Knot Colorings and Determinants

Allison Henrich; Roshni Thangavelu Truax

doi:10.2140/involve.2022.15.207

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arXiv · 2004.00148

Petal Projections, Knot Colorings and Determinants

Allison Henrich·Roshni Thangavelu Truax

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Abstract

An \"{u}bercrossing 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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Allison Henrich, Roshni Thangavelu Truax. 2020-03-31. Petal Projections, Knot Colorings and Determinants. https://doi.org/10.2140/involve.2022.15.207

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