TREE PRUNING AND LATTICE STATISTICS ON BETHE LATTICES

The method of tree pruning is employed to obtain generating functions for lattice statistics on Bethe lattices. It is shown that tree pruning significantly simplifies the evaluation of the generating function for the number of ways of placing k disjoint dimers on a Bethe lattice. Analytical expressions are derived for several Bethe lattices. An iterative algorithm is outlined for obtaining generating functions for placing dimers on a Bethe lattice of any valence a and with length n. It is further shown that the method could also be applied to weighted or anisotropic lattices.