Return words in Sturmian and episturmian words

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Return words in Sturmian and episturmian words

Considering each occurrence of a word w in a recurrent infinite word, we define the set of return words of w to be the set of all distinct words beginning with an occurrence of w and ending exactly just before the next occurrence of w in the infinite word. We give a simpler proof of the recent result (of the second author) that an infinite word is Sturmian if and only if each of its factors has...

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Sturmian and Episturmian Words (A Survey of Some Recent Results)

This survey paper contains a description of some recent results concerning Sturmian and episturmian words, with particular emphasis on central words. We list fourteen characterizations of central words. We give the characterizations of Sturmian and episturmian words by lexicographic ordering, we show how the Burrows-Wheeler transform behaves on Sturmian words. We mention results on balanced epi...

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We consider the following open question in the spirit of Ramsey theory: Given an aperiodic infinite word w, does there exist a finite coloring of its factors such that no factorization of w is monochromatic? We show that such a coloring always exists whenever w is a Sturmian word or a standard episturmian word.

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ژورنال

عنوان ژورنال: RAIRO - Theoretical Informatics and Applications

سال: 2000

ISSN: 0988-3754,1290-385X

DOI: 10.1051/ita:2000121