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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