**Lagrange Inversion and Schur Functions**, C. Lenart,*J. Algebraic Combin.***11**(2000), 69-78 (MR 01a:05149).Macdonald defined an involution on symmetric functions by considering the Lagrange inverse of the generating function of the complete homogeneous symmetric functions. The main result we prove in this note is that the images of Schur functions under this involution are either Schur positive or Schur negative symmetric functions. The proof relies on the combinatorics of Lagrange inversion. We also discuss some combinatorial aspects concerning existing formulas for the images of the complete homogeneous and the elementary symmetric functions under the involution.

Cristian Lenart, Department of Mathematics, ES 118, SUNY at Albany