ON THE D0L REPETITION THRESHOLD

The repetition threshold is a measure of the extent towhich there need to be consecutive (partial) repetitions of finite wordswithin infinite words over alphabets of various sizes. Dejean’s Conjecture,which has been recently proven, provides this threshold for allalphabet sizes. Motivated by a question of Krieger, we deal here withthe analogous threshold when the infinite word is restricted to be aD0L word. Our main result is that, asymptotically, this threshold doesnot exceed the unrestricted threshold by more than a little