Compression of transfer matrices Original Research Article

We present a method for reducing the size of transfer matrices by exploiting symmetry. For example, the transfer matrix for enumeration of matchings in the graph C4×C4×Pn can be reduced from order 65536 to 402 simply due to the 384 automorphisms of C4×C4. The matrix for enumeration of perfect matchings can be still further reduced to order 93, all in a straightforward and mechanical way. As an application we report an improved upper bound for the three-dimensional dimer problem.