On the D0L Repetition Threshold
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel;
Accepted: 20 May 2010
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.
Mathematics Subject Classification: 68R15
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