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Non-Repetitive Tilings

Show simple item record Currie, James D. Simpson, Jamie 2018-01-15T20:22:54Z 2018-01-15T20:22:54Z 2002-07-03
dc.identifier.citation Currie,James D., and Jamie Simpson. “Non-Repetitive Tilings.”,Electronic Journal of Combinatorics 9(1) (2002): Research Paper #R28. en_US
dc.identifier.issn 1077-8926
dc.description.abstract 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. en_US
dc.language.iso en en_US
dc.publisher The Electronic Journal of Combinatorics en_US
dc.title Non-Repetitive Tilings en_US
dc.type Article en_US

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