On prescribing total preorders and linear orders to pairwise distances of points in Euclidean space

Víctor Hugo Almendra-Hernández, Leonardo Martínez-Sandoval

We show that any total preorder on a set with $\left(\genfrac{}{}{0ex}{}{n}{2}\right)$ elements coincides with the order on pairwise distances of some point collection of size $n$ in ${\mathbb{R}}^{n-1}$. For…