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Episturmian words: shifts, morphisms and numeration systems. (English) Zbl 1067.68115

Summary: Episturmian words, which include the Arnoux-Rauzy sequences, are infinite words on a finite alphabet generalizing the Sturmian words and sharing many of their same properties. This was studied in previous papers. Here we gain a deeper insight into these properties. This leads in particular to consider numerations systems similar to the Ostrowski ones and to give a matrix formula for computing the number of representations of an integer in such a system. We also obtain a complete answer to the question: if an episturmian word is morphic, which shifts of it, if any, also are morphic?

MSC:

68R15 Combinatorics on words
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