Large convexly independent subsets of Minkowski sums
Large convexly independent subsets of Minkowski sums
Let $E_d(n)$ be the maximum number of pairs that can be selected from a set of $n$ points in $\mathbf{R}^d$ such that the midpoints of these pairs are convexly independent. We show that $E_2(n)\geq \Omega(n\sqrt{\log n})$, which answers a question of Eisenbrand, Pach, Rothvoß, and Sopher (2008) on large convexly …