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arXiv · 1602.05738

Periodicity and decidability of tilings of $\mathbb{Z}^{2}$

Siddhartha Bhattacharya
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Abstract

We prove that any finite set $F\subset {\mathbb{Z}^2}$ that tiles ${\mathbb{Z}^2}$ by translations also admits a periodic tiling. As a consequence, the problem whether a given finite set $F$ tiles ${\mathbb{Z}^2}$ is decidable.

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Siddhartha Bhattacharya. 2016-02-18. Periodicity and decidability of tilings of $\mathbb{Z}^{2}$. https://arxiv.org/abs/1602.05738

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