Fibonacci numbers and words

✍ Scribed by Giuseppe Pirillo

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 521 KB
• Volume: 173
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(94)00236-c

✦ Synopsis

Let 4> be the golden ratio (xf5 + 1)/2, f, the nth Fibonacci finite word and f the Fibonacci infinite word. Let r be a rational number greater than (2 + q~)/2 and u a non-empty word. If u" is a factor of f, then there exists n ~> 1 such that u is a conjugate of f. and, moreover, each occurrence of u' is contained in a maximal one of (f.)~ for some s e [2, 2 + ~b). Several known results on the Fibonacci infinite word follow from this.