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Séminaire Lotharingien de Combinatoire, B05h (1981), 1 p.

[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By making use of a result of J. Berstel (unpublished) which states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, *f*_{n} has a palindrome left factor of
length
|*f*_{n}|-2, we prove that for all *n*>=4,
*f*_{n} is the
product of two uniquely determined palindrome words, of
lengths |*f*_{n-1}|-2 and
|*f*_{n-2}|+2.
It follows that for
*n*>4 the sequence {*f*_{n}}
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 following version is available:

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