A Generalization of Repetition Threshold

Lucian Ilie, Jeffrey Shallit

Published 2003-10-10Version 1

Brandenburg and (implicitly) Dejean introduced the concept of repetition threshold: the smallest real number alpha such that there exists an infinite word over a k-letter alphabet that avoids beta-powers for all beta>alpha. We generalize this concept to include the lengths of the avoided words. We give some conjectures supported by numerical evidence and prove one of these conjectures.