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Squares and cubes in Sturmian sequences
Published online by Cambridge University Press: 06 March 2009
Abstract
We prove that every Sturmian word ω has infinitely many prefixes of the form UnVn3, where |Un| < 2.855|Vn| and limn→∞|Vn| = ∞. In passing, we give a very simple proof of the known fact that every Sturmian word begins in arbitrarily long squares.
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- © EDP Sciences, 2009
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