Close-packed dimers on nonorientable surfaces

The problem of enumerating dimers on an M x N net embedded on nonorientable surfaces is considered. We solve both the Mobius strip and Klein bottle problems for all M and N with the aid of imaginary dimer weights. The use of imaginary weights simplifies the analysis, and as a result we obtain new compact solutions in the form of double products. The compact expressions also permit us to establish a general reciprocity theorem. (C) 2002 Elsevier Science B.V. All rights reserved.