Abstract
In this talk we summarize what is known about the periodicities of strings. A period of a string is a shift that causes a string to match itself. We define z compact represention of the set of all periods of a string, called the (auto) correlation of the string. Two sets of necessary and sufficient conditions are obtained characterizing the correlations of strings. It is shown that the number of distinct correlations of strings of length n is of the order n logn. By using generating function methods we enumerate the strings having a given correlation, and investigate certain related questions. A more expanded version of these results appears in an article [0] by the author and A.M. Odlyzko.
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References
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© 1985 Springer-Verlag Berlin Heidelberg
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Guibas, L.J. (1985). Periodicities in Strings. In: Apostolico, A., Galil, Z. (eds) Combinatorial Algorithms on Words. NATO ASI Series, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82456-2_17
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DOI: https://doi.org/10.1007/978-3-642-82456-2_17
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