A Generalization of Repetition Threshold

Details A Generalization of Repetition Threshold A Generalization of Repetition Threshold

2003-10-10

arxiv.org/abs/math/0310144v1

Mathematics

Combinatorics

Scientific paper

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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