Squares and cubes in sturmian sequences

Dubickas, Artūras

doi:10.1051/ita/2009005

Geodesic

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Squares and cubes in sturmian sequences

Dubickas, Artūras

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 3, pp. 615-624

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Résumé

We prove that every sturmian word $ω$ has infinitely many prefixes of the form $U_{n} V_{n}^{3},$ where $| U_{n} | < 2.855 | V_{n} |$ and ${lim}_{n \to \infty} | V_{n} | = \infty .$ In passing, we give a very simple proof of the known fact that every sturmian word begins in arbitrarily long squares.

MR Zbl

DOI : 10.1051/ita/2009005

Classification : 68R15
Keywords: sturmian word, block-complexity, stammering word

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     title = {Squares and cubes in sturmian sequences},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {615--624},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {3},
     year = {2009},
     doi = {10.1051/ita/2009005},
     mrnumber = {2541133},
     zbl = {1176.68150},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2009005/}
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Dubickas, Artūras. Squares and cubes in sturmian sequences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 3, pp. 615-624. doi: 10.1051/ita/2009005

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