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A generator of morphisms for infinite words

Published online by Cambridge University Press:  18 October 2006

Pascal Ochem
Pascal Ochem*
Affiliation:
LaBRI, Université Bordeaux I, 351, cours de la Libération, 33405 Talence Cedex, France; ochem@labri.fr
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Abstract

We present an algorithm which produces, in some cases, infinite words avoiding both large fractional repetitions and a given set of finite words. We use this method to show that all the ternary patterns whose avoidability index was left open in Cassaigne's thesis are 2-avoidable. We also prove that there exist exponentially many $\frac{7}{4}^+$-free ternary words and $\frac{7}{5}^+$-free 4-ary words. Finally we give small morphisms for binary words containing only the squares 2, 12 and (01)² and for binary words avoiding large squares and fractional repetitions.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 3: Word Avoidability Complexity And Morphisms (WACAM) , July 2006 , pp. 427 - 441
Copyright
© EDP Sciences, 2006

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