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 gℓ(N,M) denotes the number of distinct multiplets of angular momentum ℓ and total angular momentum M, we prove thatgℓ(N,M)⩾∑k|NgL(k)Nk,M,where the sum is taken over all positive divisors of N and L(k)=kℓ-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.