Dimer statistics of honeycomb lattices on Klein bottle, Mobius strip and cylinder

Dimer statistics is a central problem in statistical physics. In this paper the enumerations of close-packed dimers of honeycomb lattices on Klein bottle, Mobius strip and cylinder are considered. By establishing a Pfaffian orientation or a crossing orientation, and then computing the determinants of the skew-symmetric matrices of the resulting orientation graphs, we obtain explicit expressions of the number of close-packed dimers of the Klein-bottle polyhex, the Mobius polyhex and the cylindrical polyhex. (C) 2012 Elsevier B.V. All rights reserved.