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
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Submitted on : Tuesday, September 26, 2006 - 9:39:07 AM Last modification on : Tuesday, December 17, 2019 - 4:16:01 PM
Gregory Kucherov, Pascal Ochem, Michael Rao. How many square occurrences must a binary sequence contain?. The Electronic Journal of Combinatorics, Open Journal Systems, 2003, 10 (1), 11 p. ⟨inria-00099596⟩