Abstract by Leslie Colton
A Compete Set of Moves on Petal Diagrams
Knots are classically represented by two dimensional diagrams where each crossing of the knot is distinct from the other crossings of the knot, i.e. two strands go into the crossing and come out of the crossing. Multi-crossing diagrams are knot diagrams where there exists a crossing such that three or more strands go into and out of the crossing, and the height of each strand inside the crossing is given by a positive integer. A petal diagram is a multi-crossing diagram with a single multi-crossing and no nested loops, and therefore is completely determined by the sequence of integers giving the multi-crossing information, which can be represented as a cycle of odd length called a "petal permutation". We find a sequence of moves on these petal permutations that is sufficient to transform a knot's petal permutation into any other petal permutation of the same knot type.