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Directive words of episturmian words: equivalences and normalization

Published online by Cambridge University Press:  22 November 2008

Amy Glen ,
Florence Levé  and
Gwénaël Richomme
Amy Glen
Affiliation:
LaCIM, Université du Québec à Montréal, C.P. 8888, succursale Centre-ville, Montréal, Québec, H3C 3P8, Canada The Mathematics Institute, Reykjavík University, Kringlan 1, IS-103 Reykjavík, Iceland; amy.glen@gmail.com
Florence Levé
Affiliation:
Université de Picardie Jules Verne, Laboratoire MIS (Modélisation, Information, Systèmes), 33 rue Saint Leu, 80039 Amiens Cedex 1, France; florence.leve@u-picardie.fr; gwenael.richomme@u-picardie.fr
Gwénaël Richomme
Affiliation:
Université de Picardie Jules Verne, Laboratoire MIS (Modélisation, Information, Systèmes), 33 rue Saint Leu, 80039 Amiens Cedex 1, France; florence.leve@u-picardie.fr; gwenael.richomme@u-picardie.fr
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Abstract

Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As a consequence of these results, we characterize episturmian words having a unique directive word.

Keywords

Episturmian wordSturmian wordArnoux-Rauzy sequenceepisturmian morphismdirective word.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 43 , Issue 2 , April 2009 , pp. 299 - 319
Copyright
© EDP Sciences, 2008

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