Exact entropy of dimer coverings for a class of lattices in three or more dimensions

Abstract

We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the method also works for graphs without translational symmetry. The partition function for dimer coverings on these lattices can be determined also for a class of assignments of different activities to different edges.

4 pages, 2 figures; added results on partition function when different edges have different weights; modified abstract; added references