#####
Séminaire Lotharingien de Combinatoire, B21m (1989), 13
pp.

[Formerly: Publ. I.R.M.A. Strasbourg, 1990, 413/S-21, p.
5-13.]

# Pierre Bouchard and Mario Ouellette

# Décomposition arborescente de Mario Ouellette

**Abstract.**
Yeong-Nan Yeh
proved the semiring (with respect to sum and product) of
(isomorphism classes of) species to be factorial, more
precisely isomorphic to the semi-ring of formal power
series **N**[[*M*]] where *M*
is the monoid (for ^{.}) of isomorphism classes of
molecular species ([Yeh]). This amounts to saying that
each species is uniquely a sum of products of atomic
species. Studying also the behavior of the
*composition* of species, Mario Ouellette ([Oue]) showed
that each species has a unique decomposition as a
composition of a primitive species and a molecular
species: this leads to a unique "arborescent"
decomposition for species. In this talk, we give a
detailed demonstration of the lemma
which is at the heart of his proof and a sketch his
proof.

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