Abstract

Several questions about relationships between borders and global and local periods of finite words are investigated in this thesis. We consider the density of critical points and applications of the critical factorization theorem. A relationship between unbordered conjugates and internal critical points is established and a border correlation function of words is investigated. Moreover, we study the relation between the global period and the length of the longest unbordered factor of a word. In particular, we resolve a longstanding conjecture called the sharpened Duval's conjecture.

Keywords: combinatorics on words, repetition, border, periodicity, critical factorization, border correlation, Duval's conjecture

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