No extremal square-free words over large alphabets
arXiv:2107.13123 · doi:10.5070/C62156889
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.
arXiv comment8 pages, no figures. Found a small mistake in Proposition 2.2 that slightly weakens our bound