A Partition Function Approximation Using Elementary Symmetric Functions
For a 4 particle system, the set of all possible microstates are partitioned into subsets of states as follows. With particle 1 as the selected particles, the microstates are first partitioned into two subsets, one with particle 1 in state and another with , with contributions to the partition function corresponding to and respectively (Eq. (3)). Each of these subsets are further partitioned into subsets with the same number of particles, , in state , with contributions to the partition function corresponding to and in Eq. (10) and (11) respectively.