中原大學應用數學系 博士學位論文 雙邊無窮 特徵 字字尾之分解 Factorizations of Suffixes of Two-Way

1. 中原大學應用數學系 博士學位論文 雙邊無窮特徵字字尾之分解 Factorizations of Suffixes of Two-Way Infinite Characteristic Words 指導教授：郭蕙芳 研 究 生：廖芳儀 組合新苗研討會_2014.8.3(日)

2. Outline 1/1 Outline • Introduction • Topic 1 Factorizations of Suffixes of Two-Way Infinite Characteristic Words • Topic 2 Markov Word Patterns in Two-Way Infinite Characteristic Words • Topic 3 Adjacent α-Words • Summaries

3. Introduction 1/10 Introduction

4. Introduction 2/10 • Different factorizations of f0

5. Introduction 3/10 • Different factorizations of f0

6. Introduction 4/10 • Different factorizations of f0

7. Introduction 5/10 • Two-way infinite characteristic words

8. Introduction 6/10 • Two-way infinite characteristic words

9. Introduction 7/10 • α-words

10. Introduction 8/10 • α-words

11. Introduction 9/10

12. Introduction 10/10 • Singular words

13. Topic 1 1/8 Topic 1

14. Topic 1 2/8 • Known results

15. Topic 1 3/8 • Our results in this thesis

16. Topic 1 4/8 • Idea Theorems 3.3.4 and 3.3.5 Theorems 3.4.1 and 3.4.2

17. Topic 1 5/8 • kth-order factorization of suffixes of and

18. Topic 1 6/8 • kth-order factorization of suffixes of and

19. Topic 1 7/8 • kth-order factorization of suffixes of and

20. Topic 1 8/8 • kth-order factorization of suffixes of and

21. Topic 2 1/5 Topic 2

22. Topic 2 2/5 • Known results

23. Topic 2 3/5 • Our results in this thesis

24. Topic 2 4/5

25. Topic 2 5/5

26. Theorem 4.1.2 Theorem 4.1.9(a) Theorem 4.1.9(b) Topic 2 5/5

27. Theorem 4.2.1 (a)(i) Theorem 4.2.1 (a)(ii) Theorem 4.2.1 (b)(i) Theorem 4.2.1 (b)(ii) Topic 2 5/5

28. Topic 3 1/5 Topic 3

29. Topic 3 2/5

30. Topic 3 3/5

31. Topic 3 3/5

32. Topic 3 4/5

33. Topic 3 4/5

34. Topic 3 4/5

35. Topic 3 5/5 • The set V

36. Summaries 1/2 Summaries • Topic 1 • Topic 2

37. Summaries 2/2 Summaries • Topic 3

38. Thanks to participate in my presentation