Polynomial versus Exponential Growth in Repetition-Free Binary Words
<|reference_start|>Polynomial versus Exponential Growth in Repetition-Free Binary Words: It is known that the number of overlap-free binary words of length n grows polynomially, while the number of cubefree binary words grows exponentially. We show that the dividing line between polynomial and exponential growth is 7/3. More precisely, there are only polynomially many binary words of length n that avoid 7/3-powers, but there are exponentially many binary words of length n that avoid (7/3+)-powers. This answers an open question of Kobayashi from 1986.<|reference_end|>
@article{karhumaki2003polynomial,
    title={Polynomial versus Exponential Growth in Repetition-Free Binary Words},
    author={Juhani Karhumaki and Jeffrey Shallit},
    journal={arXiv preprint arXiv:math/0304095},
    year={2003},
    archivePrefix={arXiv},
    eprint={math/0304095},
    primaryClass={math.CO cs.DM}
}