Expressions for the perfect matching numbers of cubic \(l\times m\times n\) lattices and their asymptotic values (Q1381251)

Begins by quoting the exact results for dimers on a plane square lattice obtained independently by M. Fisher, P. W. Kasteleyn and the reviewer in 1961. (The number of dimer arrangements without gaps is the same as the perfect matching number.) Then goes on to consider the three-dimensional cubic lattice and obtains various partial results, such as the exact number for a \(2\times m\times n\) lattice and makes various conjectures about the ``exact'' result for an \(l\times m\times n\) lattice.