Periodicity and decidability of tilings of ℤ2

By S. Bhattacharya. American Journal of Mathematics, 2020

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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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/621cf6e4e43bb2901134bff87f1ab59d56a53744