Non-Repetitive Tilings

  title={Non-Repetitive Tilings},
  author={James D. Currie and Jamie Simpson},
  journal={Electron. J. Comb.},
In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional version of this result. We show how to construct a rectangular tiling of the plane using 5 symbols which has the property that lines of tiles which are horizontal, vertical or have slope +1 or $-1$ contain no repetitions. As part of the construction we introduce a new… 

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