Exact entropy of dimer coverings of lattices in three and more dimensions

2008. június 10. kedd 14:00

In a classic paper, Kasteleyn, in 1961 showed that the calculation of the number of dimer coverings of planar lattices can be reduced to evaluating a determinant of an antisymmetric matrix. Since then, the two dimensional problem has been studied extensively. However, for three and more dimensions, only a few exact results are known. In this talk, I will deescribe the constuction of a class of lattices in two and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional Kagome lattice, and the method also works for graphs without translational symmetry.