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Issue RAIRO-Theor. Inf. Appl.
Volume 43, Number 3, July-September 2009
Page(s) 615 - 624
DOI 10.1051/ita/2009005
Published online 06 March 2009

RAIRO-Theor. Inf. Appl. 43, 615-624 (2009)
DOI: 10.1051/ita/2009005

Squares and cubes in Sturmian sequences

Artūras Dubickas

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


Received December 1st, 2008. Accepted February 5, 2009. Published online 6 March 2009

Abstract
We prove that every Sturmian word $\omega$ has infinitely many prefixes of the form UnVn3, where |Un|<2.855|Vn| and $\lim_{n\to \infty} \vert V_n\vert=\infty.$ In passing, we give a very simple proof of the known fact that every Sturmian word begins in arbitrarily long squares.


Mathematics Subject Classification. 68R15.

Key words: Sturmian word -- block-complexity -- stammering word.


© EDP Sciences 2009


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