2020/06/17 by L. A. S. Mόl, Narad Rampersad, Mol, Lucas +3 · 1 citation
Computer Science · #68R15 #Coding theory and cryptography #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Machine Learning and Algorithms #semigroups and automata theory
paper · doi:10.48550/arxiv.2006.10152
openalex publication_date 2020/06/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
An overlap-free (or β-free) word w over a fixed alphabet Σ is extremal if every word obtained from w by inserting a single letter from Σ at any position contains an overlap (or a factor of exponent at least β, respectively). We find all lengths which admit an extremal overlap-free binary word. For every extended real number β such that 2+≤β≤ 8/3, we show that there are arbitrarily long extremal β-free binary words.