English

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 β\beta-free) word ww over a fixed alphabet Σ\Sigma is extremal if every word obtained from ww by inserting a single letter from Σ\Sigma at any position contains an overlap (or a factor of exponent at least β\beta, respectively). We find all lengths which admit an extremal overlap-free binary word. For every extended real number β\beta such that 2+β8/32^+\leq\beta\leq 8/3, we show that there are arbitrarily long extremal β\beta-free binary words.

Keywords

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}
}
R2 v1 2026-06-23T16:24:59.589Z