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No extremal square-free words over large alphabets

  • Author(s): Hong, Letong;
  • Zhang, Shengtong
  • et al.

Published Web Location

https://doi.org/10.5070/C62156889Creative Commons 'BY' version 4.0 license
Abstract

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

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