Séminaire Lotharingien de Combinatoire, B14Sa (1986).

Francois Bergeron

Une combinatoire du pléthysme

Abstract. Let F(x1,x2,...) and $G(x1,x2,...) be formal power series in infinitely many variables. The plethysm FoG is the series F(G1,G2,...) where Gk(x1,x2,...) = G(x1k,x2k,...). 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.