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Directive words of episturmian words: equivalences and normalization

Published online by Cambridge University Press:  22 November 2008

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; [email protected]
Florence Levé
Affiliation:
Université de Picardie Jules Verne, Laboratoire MIS (Modélisation, Information, Systèmes), 33 rue Saint Leu, 80039 Amiens Cedex 1, France; [email protected]; [email protected]
Gwénaël Richomme
Affiliation:
Université de Picardie Jules Verne, Laboratoire MIS (Modélisation, Information, Systèmes), 33 rue Saint Leu, 80039 Amiens Cedex 1, France; [email protected]; [email protected]
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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.

Type
Research Article
Copyright
© EDP Sciences, 2008

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