On alternating knot types and their diagrams

May 25, 2023
For a given an alternating knot type K any two minimal diagrams K are related by flypes. Using flypes one can create a list of all minimal diagrams of K. What knot types have the largest or smallest number of diagrams? Many alternating knot types are curly, that means they admit a diagram without inflection points that has fewer maxima than their braid index. We show that almost all 2-bridge knots are curly. Finally, we report on a new result by Y. DIao on the rope-length of alternating knots.