On the Lattice Tilings by Lee Balls: Q-Polynomials, Group-Ring Equations, and a Decision Algorithm

Ang Xiao, Yue Zhou

More than 50 years ago, Golomb and Welch conjectured that no tilings of ${\mathbb{Z}}^n$ by Lee balls of radius $r$ exist for $n\ge 3$ and $r\ge 2$. This conjecture remains open…