Séminaire Lotharingien de Combinatoire, B05h (1981).
[Formerly: Publ. I.R.M.A. Strasbourg, 1982, 182/S-04, p. 99.]

Aldo de Luca

A Property of Fibonacci words

Abstract. By making use of a result of J. Berstel (unpublished) which states that, for n>=3, fn has a palindrome left factor of length |fn|-2, we prove that for all n>=4, fn is the product of two uniquely determined palindrome words, of lengths |fn-1|-2 and |fn-2|+2. It follows that for n>4 the sequence {fn} is the unique sequence of words satisfying the previously mentioned properties and the additional requirements that the words contain at least two different letters and that all begin with the same letter (namely, b).

The paper has been finally published under the title "A combinatorial property of the Fibonacci words" in Inform. Process. Lett. 12 (1981), 193-195.