Generating function for angular momentum multiplicities

Abstract
It is shown that the multiplicities of the total angular momentum projections for n-particle systems are given by the coefficients of certain Gaussian polynomials, for both bosons and fermions. These polynomials are parametrized in the same way as would be the corresponding binomial coefficients which solve the Bose-Einstein or Fermi-Dirac counting problems for the total number of allowed states. A comment on spin and statistics is included.

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