Cubefree binary words avoiding long squares
<|reference_start|>Cubefree binary words avoiding long squares: Entringer, Jackson, and Schatz conjectured in 1974 that every infinite cubefree binary word contains arbitrarily long squares. In this paper we show this conjecture is false: there exist infinite cubefree binary words avoiding all squares xx with |x| >= 4, and the number 4 is best possible. However, the Entringer-Jackson-Schatz conjecture is true if "cubefree" is replaced with "overlap-free".<|reference_end|>
@article{rampersad2003cubefree,
    title={Cubefree binary words avoiding long squares},
    author={Narad Rampersad, Jeffrey Shallit, Ming-wei Wang},
    journal={arXiv preprint arXiv:math/0302303},
    year={2003},
    archivePrefix={arXiv},
    eprint={math/0302303},
    primaryClass={math.CO cs.DM}
}