No extremal square-free words over large alphabets

07/28/2021

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by   Letong Hong, et al.

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A word is square-free if it does not contain any square (a word of the form XX), 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.