| Abstract (in Chinese) | 第1-5页 |
| Abstract (in English) | 第5-6页 |
| 1 Introduction | 第6-9页 |
| ·Background | 第6-7页 |
| ·Sketch of the Thesis | 第7-9页 |
| 2 The Gaussian Coefficients and Overpartitions | 第9-12页 |
| ·The Joichi-Stanton Bijection | 第9-10页 |
| ·The Involution in Interpreting Gaussian Coefficients | 第10-12页 |
| 3 Combinatorial Proof on a generalization of Schur’s Partition Theorem | 第12-15页 |
| ·Schur’s Partition Theorem and Gleissberg’s Generalizations | 第12-13页 |
| ·The Proof of (3.1.3) under an Involution | 第13-15页 |
| 4 Combinatorial Proof on Go¨llnitz’ Theorem and a Generalization | 第15-23页 |
| ·A Bijective Proof of Go¨llnitz’ Theorem | 第15-20页 |
| ·A Bijection on Some Generalizations of Go¨llnitz’ Theorem | 第20-23页 |
| 5 Some Generalizations of Partition Theorems of Schur and Go¨llnitz Type | 第23-39页 |
| ·A Four Residue Classes Partition Theorem | 第23-31页 |
| ·Partition Theorem on Five Residue Classes | 第31-35页 |
| ·A Deeper Partition Theorem | 第35-39页 |
| 6 Some Related Problems | 第39-47页 |
| ·Andrews’ Partition Theorem | 第39-40页 |
| ·Alladi, Andrews, and Berkovich’s Generalization | 第40-44页 |
| ·Partition Theorem on Other Gap Conditions | 第44-47页 |
| 7 A Conjecture on the Unimodality of a Kind of Euler Polynomials | 第47-50页 |
| ·Up-down Permutation and its q-Analogue | 第47-48页 |
| ·The Conjectures on Unimodality and Log-Concavity of A_n(q) | 第48-50页 |
| A List of A_n(q) | 第50-51页 |
| References | 第51-56页 |
| Acknowledgements | 第56页 |
