CosminPohoata

Finding the smallest integer $N=ES_d(n)$ such that in every configuration of $N$ points in $\mathbb{R}^d$ in general position, there exist $n$ points in convex position is one of the most classical problems in extremal combinatorics, known as the Erdős-Szekeres problem. In 1935, Erdős and Szekeres famously conjectured that $ES_2(n)=2^{n−2}+1$ holds, which was nearly settled by …