Abstract : Every binary word with at least four letters contains a square. A.~Fraenkel and J.~Simpson \cite{FraenkelSimpson95} showed that three {\em distinct squares} are necessary and sufficient to construct an infinite binary word. We study the following complementary question: how many {\em square occurrences} must a binary word contain? We show that this quantity is, in the limit, a constant fraction of the word length, and prove that this constant is $0.55080...$.
https://hal.inria.fr/inria-00099596
Contributeur : Publications Loria
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Soumis le : mardi 26 septembre 2006 - 09:39:07
Dernière modification le : mardi 6 mars 2018 - 17:40:57
Gregory Kucherov, Pascal Ochem, Michael Rao. How many square occurrences must a binary sequence contain?. Electronic Journal of Combinatorics, Electronic Journal of Combinatorics, 2003, 10 (1), 11 p. 〈inria-00099596〉
