An Improved Upper Bound for the ErdAs-Szekeres Conjecture
Let ES(n) denote the minimum natural number such that every set of ES(n) points in general position in the plane contains n points in convex position. In 1935, ErdAs and Szekeres proved that ES. In 1961, they obtained the lower bound , which they conjectured to be optimal. In this paper, we prove that ES(n) <= (2n - 5 n - 2) - (2n - 8 n - 3 + 2) approximate to 7/16 (2n - 4 n - 2).