On points drawn from a circle
With Steve Waton.
Advances in Applied Mathematics, to appear.
Choose n points from the unit circle, no two with the same x-coordinate or y-coordinate. Label these points 1 to n by height, reading bottom to top, and record these labels reading left to right. This operation produces a permutation. For example, the set of points shown below on the left gives the permutation 45312, the plot of which is shown on the right.
We characterise and enumerate the permutations that arise from this correspondence.