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研究生:劉洪鈞
研究生(外文):Hung Chun Liu
論文名稱:關於路徑對的一些結果
論文名稱(外文):Some Results On Path Pairs
指導教授:李陽明
指導教授(外文):Young Ming Chen
學位類別:碩士
校院名稱:國立政治大學
系所名稱:應用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:30
中文關鍵詞:路徑對不相交之路徑對
外文關鍵詞:Path pairNon-intersecting path
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在本論文中,首先定義b(n-m,k;n,k-m)為上路徑由(0,0)到(n-m,k)且下路徑由(0,0)到(n,k-m)的方法數。我們在找出b(n-m,k;n,k-m)的封閉型式後,使用最直接的數學歸納法來證明它。接著我們由b(n-m,k;n,k-m)進而找出有關它的應用,即b(n,k)及PP(n,k)。最後我們並提供一些在本文尚未解決的問題以及未來的展望。

In this thesis, our goal is to use mathematical induction to give a direct proof to show the closed form of b(n-m,k;n,k-m), where b(n-m,k;n,k-m) denotes the number of non-intersecting paths that the upper path goes from (0,0) to (n-m,k) while the lower path goes from (0,0) to (n,k-m). Furthermore, we conclude two applications about b(n-m,k;n,k-m), namely b(n,k) (see definition 2.2) and PP(n,k) (see definition 4.4). We also bring up some open problems concerning our topics.

{i} Abstract
1. Introduction}
1.1 Importance of this study
1.2 Purpose of this study
1.3 Structure of this study}
2. Literature review
3. The Number of b(n-m,k;n,k-m)
3.1 The recurrence relation of b(n-m,k;n,k-m)
3.2 The proof of b(n-m,k;n,k-m)
3.3 Example
4. Applications of b(n-m,k;n,k-m)
4.1 The number of b(n,k)
4.2 The number of PP(n,k)
5. Conclusion
6. References

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