A Generalization of Repetition Threshold
<|reference_start|>A Generalization of Repetition Threshold: 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.<|reference_end|>
@article{ilie2003a,
    title={A Generalization of Repetition Threshold},
    author={Lucian Ilie, Jeffrey Shallit},
    journal={arXiv preprint arXiv:math/0310144},
    year={2003},
    archivePrefix={arXiv},
    eprint={math/0310144},
    primaryClass={math.CO cs.DM}
}