Abstract
A closed word (a.k.a. periodic-like word or complete first return) is a word whose longest border does not have internal occurrences, or, equivalently, whose longest repeated prefix is not right special.We investigate the structure of closed factors of words. We show that a word of length n contains at least n + 1 distinct closed factors, and characterize those words having exactly n + 1 closed factors. Furthermore, we show that a word of length n can contain Θ(n 2) many distinct closed factors.
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Badkobeh, G., Fici, G., & Lipták, Z. (2015). On the number of closed factors in a word. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8977, pp. 381–390). Springer Verlag. https://doi.org/10.1007/978-3-319-15579-1_29
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