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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 whichthere need to be consecutive (partial) repetitions of finitewords within infinite wordsover alphabets of various sizes. Dejean's Conjecture, which hasbeen recently proven, provides this threshold for all alphabetsizes. Motivated by a question of Krieger, we deal here withthe analogous threshold when the infinite word is restricted to be a D0Lword. Our main result is that, asymptotically, this thresholddoes not exceed the unrestricted threshold by more than a little.

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

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