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Séminaire Lotharingien de Combinatoire, B14Sa (1986).

# Francois Bergeron

# Une combinatoire du pléthysme

**Abstract.**
Let *F*(*x*_{1},*x*_{2},...)
and $G(x_{1},*x*_{2},...)
be formal power series in infinitely many variables.
The plethysm *F*o*G* is the
series *F*(*G*_{1},*G*_{2},...)
where *G*_{k}(x_{1},*x*_{2},...) =
G(*x*_{1k},*x*_{2k},...).
Using ideas from O. Nava and G.-C. Rota [Adv. in Math. **58** (1985),
61-88], we explain the combinatorics
underlying plethysms by defining a binary operation called
substitution on **S**-species.

The paper has been finally published under the same title in
*J. Combin. Theory Ser.* A **46** (1987), 291-305.