On the Number of Closed Factors in a Word

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 $\Theta (n^2)$ many distinct closed factors.

Accepted to LATA 2015

References in corpus (4)

• Palindromic Richness
• Enumeration and Structure of Trapezoidal Words
• A new characteristic property of rich words
• Introducing Privileged Words: Privileged Complexity of Sturmian Words