Squares and cubes in Sturmian sequences
Department of Mathematics and Informatics, Vilnius University,
Naugarduko 24, Vilnius 03225, Lithuania; firstname.lastname@example.org
Accepted: 5 February 2009
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.
Mathematics Subject Classification: 68R15
Key words: Sturmian word / block-complexity / stammering word.
© EDP Sciences, 2009