I will report on this later. Observe that the lower dimensional analog is as we would expect.
Adjacency is defined exactly as before.
Another related topic is the two dimensional monomer-dimer constant . Relevant Mathcad files will be included as time permits. J. A. Bondy and D. J. A. Welsh, A note on the monomer-dimer problem, Proc. J. M. Hammersley, An improved lower bound for the multidimensional dimer problem, Proc. J. M. Hammersley and V. V. Menon, A lower bound for the monomer-dimer problem, J. Inst.