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Séminaire Lotharingien de Combinatoire, B44g (2000), 9 pp.

# Frédéric Jouhet and Jiang Zeng

#
Généralisation de Formules de Type Waring

**Abstract.**
We evaluate the symmetric functions *e*_{k},
*h*_{k} and *p*_{k} on the
alphabet {*x*_{r}/(1-*tx*_{r})}
by elementary methods and give the related generating functions.
Our formulas lead to a new and short proof of an ex-conjecture of Lassalle
[J. Combin. Theory, Series A **89** (2000), 270-288], which was
proved by Lascoux and Lassalle [Math. Annalen, to appear]
in the framework of *\lambda*-rings theory.

Received: August 14, 2000; Accepted: December 1, 2000.

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