Finding integral diagonal pairs in a two dimensional $\mathcal{N}$--set

Lev A. Borisov, Renling Jin

According to [1] an $n$-dimensional $\mathcal{N}$--set is a compact subset $A$ of ${\mathbb{R}}^n$ such that for every $x$ in ${\mathbb{R}}^n$ there is $y$ in $A$ with $y-x$ in $\mathb…