Tiling with arbitrary tiles

Vytautas Gruslys, Imre Leader, Ta Sheng Tan

Let $T$ be a tile in ${\mathbb{Z}}^n$, meaning a finite subset of ${\mathbb{Z}}^n$. It may or may not tile ${\mathbb{Z}}^n$, in the sense of ${\mathbb{Z}}^n$ having a partition into copies…