RAIRO-Theor. Inf. Appl.
Volume 46, Number 1, January-March 2012Special issue dedicated to the 13th "Journées Montoises d'Informatique Théorique"
|Page(s)||131 - 145|
|Published online||14 September 2011|
On the product of balanced sequences
University of Palermo, Dipartimento di Matematica e Informatica, Via Archirafi 34, 90123 Palermo, Italy
Received: 2 November 2010
Accepted: 11 July 2011
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.
Mathematics Subject Classification: 68R15
Key words: Infinite sequences / Sturmian words / balance / product
© EDP Sciences 2011
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