Koki Furukawa

A note on distinct volume subsets problem

For $2 \leq a \leq d+1$, what is the largest integer $H_{a,d} (n)$ such that every set of $n$ points in $\mathbb{R}^d$ with no $a$ points on a common $(a-2)$-flat contains a subset of $H_{a,d} (n)$ points whose determined $(a-1)$-dimensional simplices have pairwise distinct $(a-1)$-dimensional volumes? We construct $n$...