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Periodicity and decidability of tilings of ℤ2
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 142, Number 1, February 2020
- pp. 255-266
- 10.1353/ajm.2020.0006
- Article
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abstract:
We prove that any finite set $F\subset{\Bbb Z}^2$ that tiles ${\Bbb Z}^2$ by translations also admits a periodic tiling. As a consequence, the problem whether a given finite set $F$ tiles ${\Bbb Z}^2$ is decidable.