Squares and cubes in Sturmian sequences
Artūras Dubickas · RAIRO - Theoretical Informatics and Applications · 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.