Permutations that separate close elements, and rectangle packings in the torus

Simon R. Blackburn, Tuvi Etzion

Let $n$, $s$ and $k$ be positive integers. For distinct $i,j\in {\mathbb{Z}}_n$, define $||i,j|{|}_n$ to be the distance between $i$ and $j$ when the elements of ${\mathbb{Z}}_n$ are writ…