Directive words of episturmian words

Glen, A., Levé, F. and Richomme, G. (2008) Directive words of episturmian words. In: 12th Mons Theoretical Computer Science Days (Journées Montoises d'Informatique Théorique), 27 - 30 August, Mons, Belgium.

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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 a common episturmian word. As a consequence, we characterize episturmian words having a unique directive word.