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A method for determining the ground state of a planar interactingmany-electron system in a magnetic field perpendicular to the plane isdescribed. The ground state wave-function is expressed as a linear combinationof a set of basis functions. Given only the flux and the number of electronsdescribing an incompressible state, we use the combinatorics of partitioningthe flux among the electrons to derive the basis wave-functions as linearcombinations of Schur polynomials. The procedure ensures that the basiswave-functions form representations of the angular momentum algebra. Weexemplify the method by deriving the basis functions for the 5/2 quantum Hallstate with a few particles.

Determination of many-electron basis functions for a Quantum Hall ground state using Schur polynomials