Geodesic
Lagrange inversion and Schur functions
Journal of Algebraic Combinatorics, Tome 11 (2000) no. 1, pp. 69-78.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 skew 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 present a q-analogue of this result, which is related to the q-Lagrange inversion formula of Andrews, Garsia, and Gessel, as well as the operator $nabla$ of Bergeron and Garsia.
Keywords: Lagrange inversion, Schur function, Dyck path, Macdonald polynomials 
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     title = {Lagrange inversion and {Schur} functions},
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Lenart, Cristian. Lagrange inversion and Schur functions. Journal of Algebraic Combinatorics, Tome 11 (2000) no. 1, pp. 69-78. http://geodesic.mathdoc.fr/item/JAC_2000__11_1_a1/