Skip to main content
Open Access Publications from the University of California

Combinatorial Theory

Combinatorial Theory banner

No extremal square-free words over large alphabets

Published Web Location Commons 'BY' version 4.0 license

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 \(17\).

Mathematics Subject Classifications: 05A05, 05D10, 68R15

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View