#####
Séminaire Lotharingien de Combinatoire, B18h (1987).

[Formerly: Publ. I.R.M.A. Strasbourg, 1988, 358/S-18, p.
136-137.]

# Véronique Bruyère

# Factorization of prefix-closed subsets of words

**Abstract.**
A set of words is prefix-closed if it contains the beginning of each
word. We exhibit examples of unambiguous
factorizations (into two
sets) of such finite sets. These factorizations are completely
described here for two particular families. First, a bijection
between finite maximal
prefix codes and prefix-closed sets allows one to translate the
composition of codes into a factorization of prefix-closed
sets. Then a second
family is studied, whose examples (due to D. Perrin ) involve
asynchronous codes.

The paper has been finally published under the title
"Factorisation des ensembles préfixiels" in
*RAIRO Inform. Théor. Appl.* **23** (1989), 295-315.