How many square occurrences must a binary sequence contain?

Gregory Kucherov 1 Pascal Ochem Michael Rao 2
1 ADAGE - Applying discrete algorithms to genomics
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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 $0.55080...$.
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Electronic Journal of Combinatorics, Electronic Journal of Combinatorics, 2003, 10 (1), 11 p
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https://hal.inria.fr/inria-00099596
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Soumis le : mardi 26 septembre 2006 - 09:39:07
Dernière modification le : jeudi 11 janvier 2018 - 06:19:48

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  • HAL Id : inria-00099596, version 1

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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〉

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