#### 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
Primary: 57K10

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