English

Infinite words containing squares at every position

Combinatorics 2009-04-14 v2 Formal Languages and Automata Theory

Abstract

Richomme asked the following question: what is the infimum of the real numbers α\alpha > 2 such that there exists an infinite word that avoids α\alpha-powers but contains arbitrarily large squares beginning at every position? We resolve this question in the case of a binary alphabet by showing that the answer is α\alpha = 7/3.

Keywords

Cite

@article{arxiv.0803.1189,
  title  = {Infinite words containing squares at every position},
  author = {James D. Currie and Narad Rampersad},
  journal= {arXiv preprint arXiv:0803.1189},
  year   = {2009}
}

Comments

12 pages; minor revisions and clarifications

R2 v1 2026-06-21T10:19:45.086Z