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On the D0L Repetition Threshold

Published online by Cambridge University Press:  23 June 2010

Ilya Goldstein
Ilya Goldstein*
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel; ilyago@bgu.ac.il
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Abstract

The repetition threshold is a measure of the extent to which there need to be consecutive (partial) repetitions of finite words within infinite words over alphabets of various sizes. Dejean's Conjecture, which has been recently proven, provides this threshold for all alphabet sizes. Motivated by a question of Krieger, we deal here with the analogous threshold when the infinite word is restricted to be a D0L word. Our main result is that, asymptotically, this threshold does not exceed the unrestricted threshold by more than a little.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 3 , July 2010 , pp. 281 - 292
Copyright
© EDP Sciences, 2010

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