基本超几何级数(q-级数)理论经过两百年的发展，现在已经广泛地应用到了数论、微分方程、组合数学、统计和物理等学科分支。近一个世纪伴随着组合数学的发展，q-级数和组合数学之间的联系越来越密切。分拆理论这一门古老的学科也因为大大的推动了q-级数理论的发展而又重新回到人们的视野。本项目中我们将主要围绕分拆理论中几个经典对象：Rogers-Ramanujan-Gordo类型的分拆定理及等式，overpartition，及lecture hall分拆和anti-lecture hall有序分拆来着重展开，给出更多的关于overpartition的.Rogers-Ramanujan-Gordon类型的定理及Andrews-Gordon类型的等式，我们还将针对几个组合对象在计数方面的相互关系进行深入研究，从而给出一定的组合对应，相应的引出相关的q-级数等式。

After two hundred years of development, the basic hypergeometric series (q-series) theory has been widely applied to number theory, differential equations, combinatorics, statistics, physics and other branches. In the recent century, along with the development of combinatorial mathematics, the relation between the q-series theory and combinatorial mathematics is getting closer. Because of the promotion of the development of q-series theory, partition theory--this ancient discipline is back to people's vision. In this project, we will mainly focus on several classic problems in partition theory: theorems of the Rogers-Ramanujan-Gordon type, overpartitions, lecture hall partition and anti-lecture hall compositions。We shall give more overpartition theorems of the Rogers-Ramanujan-Gordon type and more identities of Andrews-Gordon type. Especially,we shall also focus on the relations between the enumeration of these combinatorial objections to give the combinatorial correspondence and the corresponding q-series equations.