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 has infinitely many prefixes of the form U_nV_n³, where |U_n|<2.855|V_n| and 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.


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