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A simple proof that a word of length \(n\) has at most \(2n\) distinct squares. (English) Zbl 1088.68146

Summary: We give a very short proof of a result by A. S. Fraenkel and J. Simpson [J. Comb. Theory, Ser. A 82, 112–120 (1998; Zbl 0910.05001)] which states that the number of distinct squares in a word of length \(n\) is at most \(2n\).

MSC:

68R15 Combinatorics on words

Citations:

Zbl 0910.05001
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References:

[1] Crochemore, M.; Rytter, W., Squares, cubes, and time-space efficient string searching, Algorithmica, 13, 405-425 (1995) · Zbl 0849.68044
[2] Fraenkel, A. S.; Simpson, J., How many squares can a string contain?, J. Combin. Theory, Ser. A, 82, 112-120 (1998) · Zbl 0910.05001
[3] Lothaire, M., Combinatorics on Words (1983), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0514.20045
[4] Lothaire, M., Algebraic Combinatorics on Words (2002), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1001.68093
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