Undecidability of Translational Tiling with Three Tiles
Undecidability of Translational Tiling with Three Tiles
Is there a fixed dimension $n$ such that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable? Several recent results support a positive answer to this question. Greenfeld and Tao disprove the periodic tiling conjecture by showing that an aperiodic monotile exists in sufficiently high dimension $n$ [Ann. Math. 200(2024), …