On the product of balanced sequences
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 46 (2012) no. 1, pp. 131-145.

The product w = u ⊗ v of two sequences u and v is a naturally defined sequence on the alphabet of pairs of symbols. Here, we study when the product w of two balanced sequences u,v is balanced too. In the case u and v are binary sequences, we prove, as a main result, that, if such a product w is balanced and deg(w) = 4, then w is an ultimately periodic sequence of a very special form. The case of arbitrary alphabets is approached in the last section. The partial results obtained and the problems proposed show the interest of the notion of product in the study of balanced sequences.

DOI: 10.1051/ita/2011116
Classification: 68R15
Keywords: infinite sequences, Sturmian words, balance, product
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Restivo, Antonio; Rosone, Giovanna. On the product of balanced sequences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 46 (2012) no. 1, pp. 131-145. doi : 10.1051/ita/2011116. http://www.numdam.org/articles/10.1051/ita/2011116/

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