Extremal Square-free Words
Combinatorics
2019-10-15 v1
Abstract
A word is \emph{square-free} if it does not contain non-empty factors of the form . In 1906 Thue proved that there exist arbitrarily long square-free words over -letter alphabet. We consider a new type of square-free words. A square-free word is \emph{extremal} if it cannot be extended to a new square-free word by inserting a single letter on arbitrary position. We prove that there exist infinitely many extremal words over -letter alphabet. Some parts of our construction relies on computer verifications. We also pose some related open problems.
Cite
@article{arxiv.1910.06226,
title = {Extremal Square-free Words},
author = {Jarosław Grytczuk and Hubert Kordulewski and Artur Niewiadomski},
journal= {arXiv preprint arXiv:1910.06226},
year = {2019}
}