| 摘要 | 第1-7页 |
| Abstract | 第7-12页 |
| Chapter 1 Introduction | 第12-26页 |
| ·Basic concepts | 第12-20页 |
| ·Definitions and notation of partitions and compositions | 第12-15页 |
| ·Generating functions | 第15-20页 |
| ·Euler and beyond | 第20-23页 |
| ·Overview | 第23-26页 |
| Chapter 2 Rogers-Ramanujan type identities | 第26-50页 |
| ·Introduction | 第26-30页 |
| ·Two Rogers-Ramanuj an type identities for overpartitions ... | 第30-33页 |
| ·Overpartition analogue of Theorem 2.1.3 | 第33-38页 |
| ·Combinatorial proofs of two Rogers-Ramanujan-Gordon type the-orems | 第38-50页 |
| Chapter 3 Partitions and compositions constrained by ratio of parts | 第50-92页 |
| ·Introduction | 第50-56页 |
| ·Corteel and Savages refinement of Anti-lecture Hall Theorem | 第56-60页 |
| ·Anti-lecture hall compositions and overpartitions | 第60-82页 |
| ·The proof of Theorem 3.3.2 for an even upper bound | 第63-70页 |
| ·The proof of Theorem 3.3.2 for an odd upper bound | 第70-77页 |
| ·Another proof of Theorem 3.3.7 | 第77-81页 |
| ·Further results | 第81-82页 |
| ·Lecture hall partitions with the first part bounded | 第82-87页 |
| ·A theorem related to anti-lecture hall compositions | 第87-92页 |
| References | 第92-98页 |
| 致谢 | 第98-100页 |
| 个人简历 | 第100-101页 |
