Repetition Threshold for Binary Automatic Sequences
<|reference_start|>Repetition Threshold for Binary Automatic Sequences: The critical exponent of an infinite word $\bf x$ is the supremum, over all finite nonempty factors $f$, of the exponent of $f$. In this note we show that for all integers $k\geq 2,$ there is a binary infinite $k$-automatic sequence with critical exponent $\leq 7/3$. The same conclusion holds for Fibonacci-automatic and Tribonacci-automatic sequences.<|reference_end|>
@article{allouche2024repetition,
    title={Repetition Threshold for Binary Automatic Sequences},
    author={J.-P. Allouche, N. Rampersad, J. Shallit},
    journal={arXiv preprint arXiv:2406.06513},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.06513},
    primaryClass={math.CO cs.DM cs.FL}
}