Séminaire Lotharingien de Combinatoire, B30k (1993), 10 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1993, 1993/034, p. 77-86.]

Giuseppe Pirillo

Fibonacci Numbers and Words

Abstract. Let Φ be the golden ratio (51/2+1)/2, fn the n-th Fibonacci finite word and f the Fibonacci infinite word. Let r be a rational number greater than (2+Φ)/2 and u a nonempty 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 in [2, 2 + Φ). Several known results on the Fibonacci infinite word follow from this.


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