Volumes spanned by $k$ point configurations in ${\mathbb{R}}^d$

Belmiro Galo, Alex McDonald

Given a $k$-point configuration $x\in ({\mathbb{R}}^d{)}^k$, we consider the $\left(\genfrac{}{}{0ex}{}{k}{d}\right)$-vector of volumes determined by choosing any $d$ points of $x$. We prove that a compact set…