English

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

Combinatorics 2016-02-19 v1 Dynamical Systems

Abstract

We prove that any finite set FZ2F\subset {\mathbb{Z}^2} that tiles Z2{\mathbb{Z}^2} by translations also admits a periodic tiling. As a consequence, the problem whether a given finite set FF tiles Z2{\mathbb{Z}^2} is decidable.

Keywords

Cite

@article{arxiv.1602.05738,
  title  = {Periodicity and decidability of tilings of $\mathbb{Z}^{2}$},
  author = {Siddhartha Bhattacharya},
  journal= {arXiv preprint arXiv:1602.05738},
  year   = {2016}
}