... exactly, esp ecial to lattices(maybeinfinite), such as the quadratic lattice, hexagonal lattice, triangular lattice, kagome lattice and etc[3,7,13,22]. For graph on to r us, D. J. Klein[9] had ... Enumeration of perfect matchings of a type of quadratic lattice on the torus∗Fuliang Lu Lianzhu Zhang†Fenggen LinSchool of Mathematical Sciences, Xiamen UniversityXiamen 361005, P. R. China.Zhanglz@xmu.edu.cnSubmitted: ... statistics of dimers on a lattice I: The number of dimer arrangements on a quadratic lattice, Physica 27(19 61),1209–1225]. In this paper, we generalize the result of Kasteleyn, and o bta in expressionsof...