The entropy of a monomer–dimer system on an infinite regular bipartite lattice can be written as a mean-field part plus a series expansion in the dimer density. In a previous paper it has been conjectured that all coefficients of this series are positive. Analogously on a connected regular...

We obtain explicit expressions of the number of close-packed dimers and entropy for three types of lattices (the so-called 8.8.6, 8.8.4, and hexagonal lattices) with cylindrical boundary condition and the entropy of the 8.8.6 lattice with toroidal boundary condition. Our results and the one on...