Voir la notice de l'article provenant de la source Numdam
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.
@article{ITA_2012__46_1_131_0,
author = {Restivo, Antonio and Rosone, Giovanna},
title = {On the product of balanced sequences},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {131--145},
publisher = {EDP-Sciences},
volume = {46},
number = {1},
year = {2012},
doi = {10.1051/ita/2011116},
mrnumber = {2904966},
zbl = {1247.68213},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011116/}
}
TY - JOUR AU - Restivo, Antonio AU - Rosone, Giovanna TI - On the product of balanced sequences JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 131 EP - 145 VL - 46 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2011116/ DO - 10.1051/ita/2011116 LA - en ID - ITA_2012__46_1_131_0 ER -
%0 Journal Article %A Restivo, Antonio %A Rosone, Giovanna %T On the product of balanced sequences %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 131-145 %V 46 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2011116/ %R 10.1051/ita/2011116 %G en %F ITA_2012__46_1_131_0
Restivo, Antonio; Rosone, Giovanna. On the product of balanced sequences. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 131-145. doi: 10.1051/ita/2011116
Cité par Sources :