Powers of the Vandermonde determinant and the quantum Hall effect

The expansion of the Laughlin ansatz for describing the ground-state wavefunction for the fractional quantum Hall effect as a linear combination of Slater determinantal wavefunctions for N particles is discussed in terms of the corresponding expansion of even powers of the Vandermonde alternant into Schur functions. Two new algorithms for computing the coefficients of the complete expansion are given. They appear to be substantially more efficient than other methods and avoid any use of symmetric group characters. A number of examples are given and the results obtained for N=7, 8 and 9 reviewed. The separate calculation of individual coefficients is also discussed.