Lagrange Inversion and Schur Functions
نویسنده
چکیده
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 ∇ of Bergeron and Garsia.
منابع مشابه
Identities and Positivity Conjectures for some remarkable Operators in the Theory of Symmetric Functions
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