Dimers in two dimensions

Abstract

Given a lattice, whose vertices are connected by edges, for example a square lattice, whose nearest neighbours are connected by edges in horizontal and vertical directions. The question is: In how many different ways can the edges be covered by dimers so that, at each lattice point, exactly one edge is covered by a dimer. This dimer problem can be solved for a plain lattice, if no edges cross each other. As examples, we consider the square lattice and the honeycomb lattice.