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infinite sequences

RAIRO - Theoretical Informatics and Applications (1)

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On the product of balanced sequences
Antonio Restivo, Giovanna Rosone
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 46 / Issue 1 / January 2012

Published online by Cambridge University Press:

14 September 2011, pp. 131-145

Print publication:

January 2012
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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.