Simultaneous avoidance of large squares and fractional powers in infinite binary words
Combinatorics
2007-05-23 v1 Discrete Mathematics
Abstract
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.
Cite
@article{arxiv.math/0304476,
title = {Simultaneous avoidance of large squares and fractional powers in infinite binary words},
author = {Jeffrey Shallit},
journal= {arXiv preprint arXiv:math/0304476},
year = {2007}
}