Simultaneous avoidance of large squares and fractional powers in infinite binary words
<|reference_start|>Simultaneous avoidance of large squares and fractional powers in infinite binary words: In 1976, Dekking showed that there exists an infinite binary word that contains neither squares yy with y >= 4 nor cubes xxx. We show that `cube' can be replaced by any fractional power > 5/2. We also consider the analogous problem where `4' is replaced by any integer. This results in an interesting and subtle hierarchy.<|reference_end|>
@article{shallit2003simultaneous,
    title={Simultaneous avoidance of large squares and fractional powers in
  infinite binary words},
    author={Jeffrey Shallit},
    journal={arXiv preprint arXiv:math/0304476},
    year={2003},
    archivePrefix={arXiv},
    eprint={math/0304476},
    primaryClass={math.CO cs.DM}
}