A Partition Function Approximation Using Elementary Symmetric Functions
Consider an 8-particle system, with particle 1 being the selected particle. First, the split-merge algorithm recursively separates the particles, other than the selected particle, into a hierarchical binary tree. Next, the elementary symmetric function (ESF) for the leaf nodes, which consist of a single particle, are calculated. The ESF for all the other nodes, are then computed by recursively, starting from the bottom, merging the ESF from the two branches for each node using Eq. (21).