本项目旨在研究特殊分拆函数的同余性质。分拆理论有着很强的数学物理背景，吸引了包括美国科学院院士George Andrews教授、中国科学院院士陈永川教授在内的众多著名组合、数论专家的研究兴趣。分拆函数的同余性质是当代组合学研究的前沿课题之一。.. 项目将利用 Ramanujan theta 函数等式、模形式与组合方法这三大工具，研究一些特殊分拆函数的同余性质，如：着色广义 Frobenius 分拆、偶数部分互不相同的双分拆、断裂k-钻石分拆和奇异带杠分拆，并解决一些公开问题。.. 在项目的实施过程中，我们期望利用上面的三个方法，不仅能够证明一些分拆同余式的猜想，发现更多的分拆同余式，而且还期望能给出分拆同余式的组合解释和组合证明。项目的研究成果将丰富分拆同余式的相关理论，为分拆理论在q-级数、组合数学、数论和物理学等领域的应用提供更多的理论支持。

The main objective of this proposal is to study the congruence properties of some special partition functions. The theory of partitions has a strong background in mathematical physics, and attracted the attention of many experts in combinatorics and number theory, including Professor Andrews George who is an elected member of American Academy of Arts and Sciences and Professor Yongchuan Chen who is an Academician of Chinese Academy of Sciences. Study on congruence properties of partition functions is one of the most active fields in contemporary combinatorics... The project will use the three tools, that is Ramanujan theta function identities, modular forms and combinatorial methods, to study congruence properties of some special partition functions, such as colored generalized Frobenius partitions, bipartitions with distinct even parts, broken k-diamond partitions and singular overpartitions. In addition, we will try to solve some open problems... In the process of implementation of the project, we expect to use the above three methods, not only to prove some conjectures on partition congruences and discover more congruences of partitions, but also to give combinatorial interpretation and combinatorial proofs of partition congruences. The research results of the project will enrich the theory of partition congruences, and provide more theoretical supports for applications of the theory of partitions in the fields of q-series, combinatorics, physics and so on.