Geodesic
Fibonacci Numbers and Words
Séminaire lotharingien de combinatoire, Tome 30 (1993) 
Giuseppe Pirillo. Fibonacci Numbers and Words. Séminaire lotharingien de combinatoire, Tome 30 (1993). http://geodesic.mathdoc.fr/item/SLC_1993_30_a10/
@article{SLC_1993_30_a10,
     author = {Giuseppe Pirillo},
     title = {Fibonacci {Numbers} and {Words}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {1993},
     volume = {30},
     url = {http://geodesic.mathdoc.fr/item/SLC_1993_30_a10/}
}
TY  - JOUR
AU  - Giuseppe Pirillo
TI  - Fibonacci Numbers and Words
JO  - Séminaire lotharingien de combinatoire
PY  - 1993
VL  - 30
UR  - http://geodesic.mathdoc.fr/item/SLC_1993_30_a10/
ID  - SLC_1993_30_a10
ER  - 
%0 Journal Article
%A Giuseppe Pirillo
%T Fibonacci Numbers and Words
%J Séminaire lotharingien de combinatoire
%D 1993
%V 30
%U http://geodesic.mathdoc.fr/item/SLC_1993_30_a10/
%F SLC_1993_30_a10

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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.