  A method for determining the ground state of a planar interacting
many-electron system in a magnetic field perpendicular to the plane is
described. The ground state wave-function is expressed as a linear combination
of a set of basis functions. Given only the flux and the number of electrons
describing an incompressible state, we use the combinatorics of partitioning
the flux among the electrons to derive the basis wave-functions as linear
combinations of Schur polynomials. The procedure ensures that the basis
wave-functions form representations of the angular momentum algebra. We
exemplify the method by deriving the basis functions for the 5/2 quantum Hall
state with a few particles.
