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No extremal square-free words over large alphabets
arXiv - CS - Discrete Mathematics Pub Date : 2021-07-28 , DOI: arxiv-2107.13123
Letong Hong, Shengtong Zhang

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 15.

中文翻译:

大字母表上没有无极值的无方词

如果一个词不包含任何方格(形式为 $XX$ 的词),则该词是无方格的,如果不能通过在任何位置插入一个字母来扩展为新的无方格词,则该词是无方格的. Grytczuk、Kordulewski 和 Niewiadomski 证明了存在无限多个三元极值无平方词。我们确定在任何大小至少为 15 的字母表上都没有极值无平方词。
更新日期:2021-08-03
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