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math.CO2026
The Golomb--Welch conjecture for arbitrary centre sets
Bocong Chen, Jing Huang, Gaojun Luo
We prove that for all and , the Lee ball does not tile by translations, resolving the Golomb--Welch conjecture for arbitrary centre sets and completi…
cs.IT2026
The Golomb--Welch conjecture for lattice tilings
Bocong Chen, Jing Huang, Gaojun Luo
We prove the Golomb--Welch conjecture for lattice tilings: for every and , the integer lattice admits no lattice tiling by Lee balls of radius . T…