Squares and cubes in sturmian sequences
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 3, pp. 615-624.

We prove that every sturmian word ω has infinitely many prefixes of the form U n V n 3 , where |U n |<2.855|V n | and lim n |V n |=. In passing, we give a very simple proof of the known fact that every sturmian word begins in arbitrarily long squares.

DOI: 10.1051/ita/2009005
Classification: 68R15
Keywords: sturmian word, block-complexity, stammering word
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Dubickas, Artūras. Squares and cubes in sturmian sequences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 3, pp. 615-624. doi : 10.1051/ita/2009005. http://www.numdam.org/articles/10.1051/ita/2009005/

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