Periodicity and unbordered words: A proof of the extended duval conjecture

The relationship between the length of a word and the maximum length of its unbordered factors is investigated in this paper. Consider a finite word w of length n. We call a word bordered if it has a proper prefix which is also a suffix of that word. Let µ(w) denote the maximum length of all unbordered factors of w, and let ∂(w) denote the period of w. Clearly, µ(w) ≤ ∂(w).

• Type: Journal
• Year: 2007
• Where: JACM
• Authors: Tero Harju, Dirk Nowotka
• Keywords: JACM 2007, Maximum Length, Unbordered Factors, finite Word