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A Generalization of Repetition Threshold

Lucian Ilie·Jeffrey Shallit
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Abstract

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.

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Lucian Ilie, Jeffrey Shallit. 2003-10-10. A Generalization of Repetition Threshold. https://arxiv.org/abs/math/0310144

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