Generalizing the Quinn-Wójs theorem on distinct multiplets of composite Fermions

The combinatorial tool of generating functions for restricted partitions is used to generalize a quantum physics theorem relating distinct multiplets of different angular momenta in the composite Fermion model of the fractional quantum Hall effect. Specifically, if g (N,M) denotes the number of distinct multiplets of angular momentum and total angular momentum M, we prove that g (N,M) ∑ k|N gL(k) ( N k ,M ) , where the sum is taken over all positive divisors ofN andL(k)=k −kN/2+3k/2−N+N/(2k)−1/2. The original Quinn–Wójs theorem results when k = 1 and it appears that this generalization will be useful in further investigations of nuclear shells modeling elementary particle interactions when the particles are clustered together. © 2005 Elsevier B.V. All rights reserved.