Extremal overlap-free and extremal $\beta$-free binary words
Combinatorics
2020-06-19 v1 Discrete Mathematics
Formal Languages and Automata Theory
Abstract
An overlap-free (or -free) word over a fixed alphabet is extremal if every word obtained from by inserting a single letter from at any position contains an overlap (or a factor of exponent at least , respectively). We find all lengths which admit an extremal overlap-free binary word. For every extended real number such that , we show that there are arbitrarily long extremal -free binary words.
Cite
@article{arxiv.2006.10152,
title = {Extremal overlap-free and extremal $\beta$-free binary words},
author = {Lucas Mol and Narad Rampersad and Jeffrey Shallit},
journal= {arXiv preprint arXiv:2006.10152},
year = {2020}
}