No extremal square-free words over large alphabets
Combinatorics
2023-02-07 v2 Discrete Mathematics
Abstract
A word is square-free if it does not contain any square (a word of the form ), and is extremal square-free if it cannot be extended to a new square-free word by inserting a single letter at any position. Grytczuk, Kordulewski, and Niewiadomski proved that there exist infinitely many ternary extremal square-free words. We establish that there are no extremal square-free words over any alphabet of size at least 17.
Cite
@article{arxiv.2107.13123,
title = {No extremal square-free words over large alphabets},
author = {Letong Hong and Shengtong Zhang},
journal= {arXiv preprint arXiv:2107.13123},
year = {2023}
}
Comments
8 pages, no figures. Found a small mistake in Proposition 2.2 that slightly weakens our bound