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Theoretical Computer Science
Volume 340, Issue 2, 27 June 2005, Pages 204-219
The Art of Theory
 
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doi:10.1016/j.tcs.2005.03.020    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2005 Elsevier B.V. All rights reserved.

Words derivated from Sturmian words

Isabel M. Araújoa, 1, E-mail The Corresponding Author and Véronique Bruyèreb, Corresponding Author Contact Information, E-mail The Corresponding Author

aDepartamento de Matemática, Universidade de Évora Rua Romão Ramalho, 59, 7000-671 Évora, Portugal bInstitut d’Informatique, Université de Mons-Hainaut, Le Pentagone av. du Champ de Mars, 6, 7000 Mons, Belgium

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


Theoretical Computer Science
Volume 340, Issue 2, 27 June 2005, Pages 204-219
The Art of Theory
 
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