Searching for authors named "James Currie" – sorted by Relevance.
6 documents found, showing 1 through 6.
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Non-repetitive Tilings
- …In 1906 Axel Thue showed how to construct an in nite non-repetitive (or squarefree) 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…
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No iterated morphism generates any Arshon sequence of odd order
- …We show that no Arshon sequence of odd order can be generated by an iterated morphism. This solves a problem of Kitaev and generalizes results of Berstel and of Kitaev. Keywords: Combinatorics on words, non-repetitive words, Arshon’s sequence, DOL systems 1…
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There Are Ternary Circular Square-Free Words of Length n for n ≥ 18
- …There are circular square-free words of length n on three symbols for n 18. This proves a conjecture of R. J. Simpson.…
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Extremal Infinite Overlap-Free Binary Words
- …Let t be the infinite fixed point, starting with 1, of the morphism :0#01, 1 # 10. An infinite word over {0, 1} is said to be overlap-free if it contains no factor of the form axaxa, where a #{0,1}and x #{0,1} # . We prove that the lexicographically least infinite overlap-free binary word begi…
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Article 04.2.7
- …We show that the number of ternary words of length n avoiding abelian cubes grows faster than r , where r = 2 1=24 .…
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Separating Words with Small Grammars
- …We study the following problem: given two words w and x, with jwj; jxj n, what is the size of the smallest context-free grammar G which generates exactly one of fw; xg? If jwj 6= jxj, then we prove there exists a G separating w from x of size O(log log n), and this bound is best possible. If jwj …
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