Petal projections, knot colorings and determinants

An \"{u}bercrossing diagram is a knot with only one crossing that may involve more than two strands of the knot. Such without any nested loops called petal projection. Every has projection from which can be recovered using permutation represents strand heights. Using this permutation, we give an algorithm determines $p$-colorability and determinants knots their projections. In particular, compute all prime number less $10$ permutations.