Periods in strings

Leo J. Guibas; Andrew M. Odlyzko

doi:10.1016/0097-3165(81)90038-8

Periods in strings

Leo J. Guibas, Andrew M. Odlyzko

School of Mathematics

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123 Scopus citations

Abstract

In this paper we explore the notion of periods of a string. A period can be thought of as a shift that causes the string to match over itself. We obtain two sets of necessary and sufficient conditions for a set of integers to be the set of periods of some string (what we call the correlation of the string). We show that the number of distinct correlations of length n is independent of the alphabet size and is of order n^logn. By using generating function methods we enumerate the strings having a given correlation, and investigate certain related questions.

Original language	English (US)
Pages (from-to)	19-42
Number of pages	24
Journal	Journal of Combinatorial Theory, Series A
Volume	30
Issue number	1
DOIs	https://doi.org/10.1016/0097-3165(81)90038-8
State	Published - Jan 1981

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Periods in strings

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