Forced convex \(n\)-gons in the plane (Q1387846)

Denote by \(g(n)\) the smallest number such that every set of \(g(n)\) points in the plane in general position contains the vertices of a convex \(n\)-gon. In 1935 Erdős and Szekeres proved that \[ 2^{n- 2}+ 1\leq g(n)\leq {2n-4\choose n-2}+ 1. \] The authors of the present paper lessen the right estimate by 1.