Extremal square-free words
Jarosław Grytczuk , Hubert Kordulewski , A. Niewiadomski
AbstractA word is square-free if it does not contain nonempty factors of the form XX. In 1906 Thue proved that there exist arbitrarily long square-free words over a 3-letter alphabet. We consider a new type of square-free words with additional property. A square-free word is called extremal if it cannot be extended to a new square-free word by inserting a single letter at any position. We prove that there exist infinitely many square-free extremal words over a 3-letter alphabet. Some parts of our construction relies on computer verifications. It is not known if there exist any extremal square-free words over a 4-letter alphabet.
|Journal series||Electronic Journal of Combinatorics, ISSN 1077-8926|
|Publication size in sheets||0.5|
|Keywords in Polish||Ekstremalne słowa bez repetycji|
|Keywords in English||Extremal square-free words|
|ASJC Classification||; ;|
|Abstract in Polish||Praca dowodzi istnienia nieskończenie wielu słów ekstremalnych nad alfabetem 3-literowym.|
|Score||= 100.0, 26-06-2020, ArticleFromJournal|
|Publication indicators||= 0; : 2018 = 0.922; : 2018 = 0.762 (2) - 2018=0.764 (5)|
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