Directive words of episturmian words: equivalences and normalization

Amy Glen (1, 2) , Florence Levé (3) , Gwenaël Richomme (3, 4, 5)

1 LaCIM - Laboratoire de combinatoire et d'informatique mathématique [Montréal]
2 The Mathematics Institute
3 MIS - Modélisation, Information et Systèmes - UR UPJV 4290
4 ARITH - Arithmétique informatique
5 UPVM - Université Paul-Valéry - Montpellier 3

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.

Domaines: Mathématique discrète [cs.DM]

Amy Glen, Florence Levé, Gwenaël Richomme. Directive words of episturmian words: equivalences and normalization. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2009, 43 (2), pp.299-319. ⟨10.1051/ita:2008029⟩. ⟨hal-00599746⟩