| Table of Contents | 第1-4页 |
| Abstract (in English) | 第4-6页 |
| 中文摘要 | 第6-7页 |
| Acknowledgements | 第7-9页 |
| Introduction | 第9-13页 |
| 1 Preliminaries | 第13-23页 |
| ·Permutations with Forbidden Patterns | 第13-15页 |
| ·Canonical Reduced Decompositions | 第15-17页 |
| ·Lattice Paths | 第17-20页 |
| ·Tables for Some Known Results | 第20-23页 |
| 2 Dyck Paths and Permutations with Forbidden Patterns | 第23-35页 |
| ·Canonical Reduced Decompositions for S_n(321) | 第23-25页 |
| ·Staircase Decompositions for Dyck Paths | 第25-28页 |
| ·Canonical Reduced Decompositions for S_n(231) | 第28-30页 |
| ·Trapezoidal Decompositions for Dyck Paths | 第30-33页 |
| ·Fine Paths and Derangements with Forbidden Patterns | 第33-35页 |
| 3 Motzkin Paths and Permutations with Forbidden Patterns | 第35-45页 |
| ·Canonical Reduced Decompositions for S_n (321,31|-42) | 第36-37页 |
| ·Staircase Decompositions for Motzkin Paths | 第37-41页 |
| ·Canonical Reduced Decompositions for S_n(231,41|-32) | 第41-42页 |
| ·Trapezoidal Decompositions for Motzkin Paths | 第42-45页 |
| 4 Riordan Paths and Derangements with Forbidden Patterns | 第45-50页 |
| ·Riordan Paths | 第46-47页 |
| ·Riordan Paths and Derangements with Forbidden Patterns | 第47-50页 |
| 5 Schroder Paths and Permutations with Forbidden Patterns | 第50-55页 |
| ·Schroder Paths and S_(n+1)(4231,4132) | 第51-52页 |
| ·Schroder Paths and S_(n+1) (3421,3412) | 第52-55页 |
| 6 Discrete Continuity | 第55-59页 |
| Bibliography | 第59-64页 |
