The infamous Erdos-Szekeres Conjecture states that the number of points on a plane in general position with no n (greater than 1) points in convex position, called an n-gon, is at most 2^(n-2).
They later provided a construction S_n of exactly that many points avoiding any such n-gon.

Erdos, Tuza and Valtr discovered that, if the conjecture is true, the 'interval' subset S_{n, a, b} of the maximal construction S_n should also attain the maximum size while avoiding any n-gon, a-cap or b-cup for a, b Speaker(s): Jin Baek (UM)