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 ek,
hk and pk on the
alphabet {xr/(1-txr)}
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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