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

TL;DR

This paper introduces a method to exactly compute the number of dimer coverings on certain high-dimensional lattices, generalizing known 2D results and applicable even without translational symmetry.

Contribution

It presents a novel approach to exactly determine dimer covering counts on complex high-dimensional lattices, extending previous 2D lattice results.

Findings

Exact enumeration of dimer coverings for specific high-dimensional lattices

Method applicable to graphs lacking translational symmetry

Partition function can incorporate varied edge activities

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.