Fibonacci numbers and words Original Research Article

Let Φ be the golden ratio (√5 + 1)/2, fn the nth Fibonacci finite word and f the Fibonacci infinite word. Let r be a rational number greater than (2 + Φ)/2 and u a nondashempty word. If ur is a factor of f, then there exists n ⩾ 1 such that u is a conjugate of fn and, moreover, each occurrence of ur is contained in a maximal one of (fn)s for some s ∈ [2, 2 + Φ). Several known results on the Fibonacci infinite word follow from this.