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Episturmian words and episturmian morphisms. (English) Zbl 1002.68116

Summary: Infinite episturmian words are a generalization of Sturmian words which includes the Arnoux-Rauzy sequences. We continue their study and that of episturmian morphisms, begun previously, in relation with the action of the shift operator. Palindromic and periodic factors of these words are described. We consider, in particular, the case where these words are generated by morphisms and introduce then a notion of intercept generalizing that of Sturmian words. Finally, we prove that the frequencies of the factors in a strong sense do exist for all episturmian words.

MSC:

68R15 Combinatorics on words
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