PDF

Lagrange Inversion and Schur Functions

CRISTIAN LENART

2026enLagrange inversionSchur functionssymmetric functionscombinatoricsDyck pathsMacdonald polynomials

Abstract

Language:

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.

Download

Cite This Work

@article{8694ed47-1655-4df8-810f-ccea6ad6464b,
  title={Lagrange Inversion and Schur Functions},
  author={CRISTIAN LENART},
  year={2026},
  language={en}
}
TY  - JOUR
TI  - Lagrange Inversion and Schur Functions
AU  - CRISTIAN LENART
PY  - 2026
LA  - en
ER  -

Similar Items

Optimization of Integrated Steel Plant R

This paper addresses the challenge of assessing the feasibility of wind power plant projects at sites with insufficient or no local historic wind data

2025enPDF

Design for Recovery of Precious and Base

2026enPDF

Electrochemical techniques for a cleaner

Important advances in electrochemical engineering technology over the last three decades have fostered the development of a lternative methods to alle

2026enPDF

Environmental and Human Health Risks Ass

2026enPDF

The Recovery of Precious and Base Metals

Increasing volumes of waste printed circuit boards from obsolete electronic equipment posed escalating environmental risks and resource losses due to

2026enPDF

Treatment of manufacturing scrap TV boar

The leachability tests for manufacturing scrap TV boards (STVB) have indicated the release of metals beyond the limit levels with potential problems f

2026enPDF