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.

Restivo, A., Rosone, G. (2012). On the product of balanced sequences. RAIRO. INFORMATIQUE THEORIQUE ET APPLICATIONS, 46(1), 131-145 [10.1051/ita/2011116].

On the product of balanced sequences

RESTIVO, Antonio;ROSONE, Giovanna
2012-01-01

Abstract

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.
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8509855
Restivo, A., Rosone, G. (2012). On the product of balanced sequences. RAIRO. INFORMATIQUE THEORIQUE ET APPLICATIONS, 46(1), 131-145 [10.1051/ita/2011116].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/65676
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