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Squares and cubes in Sturmian sequences

Published online by Cambridge University Press:  06 March 2009

Artūras Dubickas
Artūras Dubickas*
Affiliation:
Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius 03225, Lithuania; arturas.dubickas@mif.vu.lt
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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.

Keywords

Sturmian wordblock-complexitystammering word.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 3 , July 2009 , pp. 615 - 624
Copyright
© EDP Sciences, 2009

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