Dimer statistics on a Möbius strip

A closed-form expression is obtained for the generating function of close-packed dimers on a $2M \times 2N$ simple quartic lattice embedded on a M\"obius strip. The finite-size corrections are also analyzed and compared with those under cylindrical and free boundary conditions. Particularly, it is found that, for large lattices with a square symmetry and the M\"obius boundary condition, the number of dimer configurations is 70.2% of that under the cylindrical boundary condition. Results for the Klein bottle are also given.