Geodesic
Non-repetitive tilings
The electronic journal of combinatorics, Tome 9 (2002)
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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 type of word, one that is non-repetitive up to mod k, which is of interest in itself. We also indicate how our results might be extended to higher dimensions.
DOI : 10.37236/1644
Classification : 05B45, 05B30, 11B99
Mots-clés : rectangular tiling of the plane 
@article{10_37236_1644,
     author = {James D. Currie and Jamie Simpson},
     title = {Non-repetitive tilings},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1644},
     zbl = {1004.05020},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1644/}
}
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James D. Currie; Jamie Simpson. Non-repetitive tilings. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1644

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