On convex permutations
With Michael Albert, Steve Linton, Nik Ruskuc, and Steve Waton.
Discrete Mathematics, 311 (2011), 715–722.
A selection of points drawn from a convex polygon, no two with the same vertical or horizontal coordinate, yields a permutation in a canonical fashion. We characterise and enumerate those permutations which arise in this manner and exhibit some interesting structural properties of the closed class they form. We conclude with a permutation analogue of the celebrated Happy Ending Problem.