Constraints on the two-particle distribution function due to the permutational symmetry of the higher order distribution functions

We investigate how the range of parameters that specify the two-particle distribution function is restricted if we require that this function be obtained from the $n^{rm th}$ order distribution functions that are symmetric with respect to the permutation of any two particles. We consider the simple case when each variable in the distribution functions can take only two values. Results for all $n$ values are given, including the limit of $ntoinfty$. We use our results to obtain bounds on the allowed values of magnetization and magnetic susceptibility in an $n$ particle Fermi fluid.