Copyright © 2005 Elsevier B.V. All rights reserved.
Words derivated from Sturmian words
Available online 6 April 2005.
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Abstract
A return word of a factor of a Sturmian word starts at an occurrence of that factor and ends exactly before its next occurrence. Derivated words encode the unique decomposition of a word in terms of return words. Vuillon has proved that each factor of a Sturmian word has exactly two return words. We determine these two return words, as well as their first occurrence, for the prefixes of characteristic Sturmian words. We then characterize words derivated from a characteristic Sturmian word and give their precise form. Finally, we apply our results to obtain a new proof of the characterization of characteristic Sturmian words which are fixed points of morphisms.
Keywords: Combinatorics on words; Sturmian words; Return words







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(0,1) is an irrational. As
1. It is well known that an aperiodic word is Sturmian if and only if it is balanced.





