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Journal Articles The Electronic Journal of Combinatorics Year : 2003

How many square occurrences must a binary sequence contain?

Pascal Ochem
Michael Rao

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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Other [cs.OH]

Dates and versions

inria-00099596 , version 1 (26-09-2006)

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Gregory Kucherov, Pascal Ochem, Michael Rao. How many square occurrences must a binary sequence contain?. The Electronic Journal of Combinatorics, 2003, 10 (1), 11 p. ⟨10.37236/1705⟩. ⟨inria-00099596⟩
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