The repetition threshold for ternary rich words
<|reference_start|>The repetition threshold for ternary rich words: In 2014, Vesti proposed the problem of determining the repetition threshold for infinite rich words, i.e., for infinite words in which all factors of length $n$ contain $n$ distinct nonempty palindromic factors. In 2020, Currie, Mol, and Rampersad proved a conjecture of Baranwal and Shallit that the repetition threshold for binary rich words is $2 + \sqrt{2}/2$. In this paper, we prove a structure theorem for $16/7$-power-free ternary rich words. Using the structure theorem, we deduce that the repetition threshold for ternary rich words is $1 + 1/(3 - \mu) \approx 2.25876324$, where $\mu$ is the unique real root of the polynomial $x^3 - 2x^2 - 1$.<|reference_end|>
@article{currie2024the,
    title={The repetition threshold for ternary rich words},
    author={James D. Currie, Lucas Mol, and Jarkko Peltom"aki},
    journal={arXiv preprint arXiv:2409.12068},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.12068},
    primaryClass={math.CO cs.DM cs.FL}
}