Geodesic
How many square occurrences must a binary sequence contain?
The electronic journal of combinatorics, Tome 10 (2003)
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Every binary word with at least four letters contains a square. A. Fraenkel and J. Simpson showed that three distinct squares are necessary and sufficient to construct an infinite binary word. We study the following complementary question: how many 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 $0.55080...$.
DOI : 10.37236/1705
Classification : 05A15, 68R15 
@article{10_37236_1705,
     author = {Gregory Kucherov and Pascal Ochem and Micha\"el Rao},
     title = {How many square occurrences must a binary sequence contain?},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1705},
     zbl = {1011.05007},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1705/}
}
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Gregory Kucherov; Pascal Ochem; Michaël Rao. How many square occurrences must a binary sequence contain?. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1705

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