Borders Of Fibonacci Strings

L.J. Cummings1, D. Moore2, J. Karhumakit 3
1University of Waterloo
2 Curtin University of Technology
3Turku University

Abstract

We determine all borders of the \(n\underline{th}\) Fibonacci string, \(f_n\), for \(n \geq 3\). In particular, we give two proofs that the longest border of \(f_n\) is \(f_{n-2}\). One proof is independent of the Defect Theorem.