| Abstract (in Chinese) | 第1-7页 |
| Abstract (in English) | 第7-12页 |
| 1 Introduction | 第12-32页 |
| ·Notations and Backgrounds | 第12-27页 |
| ·Main Results and Structure of This Thesis | 第27-32页 |
| 2 Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions | 第32-42页 |
| ·k-tuples of Noncrossing Free Dyck Paths and Plane Partitions | 第32-33页 |
| ·Pairs of Noncrossing Free Dyck Paths | 第33-39页 |
| ·The Labelle Merging Algorithm | 第39-42页 |
| 3 Uniform Distribution of m-free Schroder Paths and Free Dyck Paths | 第42-60页 |
| ·Some Studies on Flaw Number | 第42-55页 |
| ·m-free Schroder Paths on Absolute Minimum Length | 第55-56页 |
| ·Free Dyck Paths on Absolute Minimum Length | 第56-60页 |
| 4 Partial k-Dyck Paths with a Given Type | 第60-74页 |
| ·The Enumeration on Partial k-Dyck Paths with a Given Type | 第60-65页 |
| ·Application to Noncrossing Partitions | 第65-68页 |
| ·Parking Functions, Labeled Dyck Paths, and Rooted Forests | 第68-74页 |
| 5 Interesting Chung-Feller Properties in a Quarter of Plane | 第74-80页 |
| Bibliography | 第80-86页 |
| 致谢 | 第86-88页 |
| 个人简介 | 第88页 |
