图的生成树计数与Dimer 问题是组合学与统计物理中两个基本且重要的问题，受到组合学家与统计物理学家的密切关注。本项目主要研究统计物理学家重点关注的格子系统中的Dimer 问题与生成树的计数问题；完善阿基米德格子（Archimedean lattices）及其对偶图-Lave 格子（Lave lattices）的生成树及完美匹配或所有匹配的计数问题，以及这些格子图计数问题之间的联系，包括研究它们的计数公式，以及在统计物理意义下自由能与熵的解析表达式。本项目的预期成果将为统计物理学的研究提供可能的数学理论依据，其具有学科交叉的性质和多方面的应用背景。

The counting of spanning trees and Dimer problems are two basic and important problems in combinatorics and statistical physics, which is focused on by combinatorialists and statistical physicists.This project mainly focuses on the Dimer problems and the counting problems of spanning tree in the lattice systems which are concerned by physicists; And improve the counting problems of the spanning tree, perfect matching or all the matching of the Archimedean lattices and its dual graph-Lave lattices. Research the relationship between these counts, including their counting formulas, as well as the analytic expressions of free energy and entropy in the sense of statistical physics. The expected results of this project will provide possible theoretical basis of mathematics for the study of statistical physics, it has the character of interdisciplinary and a wide range of applications.