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{\bf Gregory Kucherov, Pascal Ochem and Micha\"el Rao}
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{\bf How Many Square Occurrences Must a Binary Sequence Contain?}
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Every binary word with at least four letters contains a square. A.~Fraenkel
and J.~Simpson showed that three {\it distinct
squares} are necessary and sufficient to construct an infinite binary word.
We study the following complementary question: how many {\it 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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