Geodesic
How many squares must a binary sequence contain?
The electronic journal of combinatorics, Tome 2 (1995)
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Let $g(n)$ be the length of a longest binary string containing at most $n$ distinct squares (two identical adjacent substrings). Then $g(0)=3$ (010 is such a string), $g(1)=7$ (0001000) and $g(2)=18$ (010011000111001101). How does the sequence $\{g(n)\}$ behave? We give a complete answer.
DOI : 10.37236/1196
Classification : 11A67, 11K16
Mots-clés : length, longest binary string, distinct squares 
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     author = {Aviezri S. Fraenkel and R. Jamie Simpson},
     title = {How many squares must a binary sequence contain?},
     journal = {The electronic journal of combinatorics},
     year = {1995},
     volume = {2},
     doi = {10.37236/1196},
     zbl = {0816.11007},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1196/}
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Aviezri S. Fraenkel; R. Jamie Simpson. How many squares must a binary sequence contain?. The electronic journal of combinatorics, Tome 2 (1995). doi: 10.37236/1196

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