The Golomb--Welch conjecture for arbitrary centre sets

Bocong Chen, Jing Huang, Gaojun Luo

We prove that for all $n\ge 3$ and $r\ge 2$, the Lee ball $B_n(r)$ does not tile ${\mathbb{Z}}^n$ by translations, resolving the Golomb--Welch conjecture for arbitrary centre sets and completi…