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https://nccur.lib.nccu.edu.tw/handle/140.119/87368
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| Title: | Catalan數的對射證明
A Bijective Proof of Catalan Number |
| Authors: | 李英杰
Lee, Ing-Jye |
| Contributors: | 李陽明
Li, Young-Ming
李英杰
Lee, Ing-Jye |
| Keywords: | 生成函數
對射函數
二元樹
Catalan數(族)
Catalan number |
| Date: | 1996 |
| Issue Date: | 2016-04-28 13:30:01 (UTC+8) |
| Abstract: | 本文的主旨是利用對射函數的方法,證明圓周上2n個點成功配對問題的解是Catalan數.所以必須找一個也是Catalan數的事物來和本問題對應,這裡找的是n個節點的二元數.我們先造一個由成功配對應射到二元數的函數,再證明此函數是一對一且映成,既為對射函數,則我們就可以知道成功配對的解是Catalan數.然後再將問題推廣到3n個點,甚至到kn個點的情形,以得到一般的問題解. |
| Reference: | [1] C. Berge, (1971), Principles of Combinatorics, Academic
Press,New York.
[2] Ri chard A. Brualdi, (1977),Introductory Combinatorics, New York,Elsevier Science Publishing Co. ,Inc.
[3] Ronald L.Graham,Donald E.Knuth,Oren Patashnik,(19S9),
Concrete Mathematics, Addison-Wesley Publ ishing Co. , Inc.
[4] Ralph P. Grimaldi, (1985) ,Discrete and Combinat0l1al
Mathematics,Addison-Wesley Publishing Co., Inc.
[5] Marshall Jr. Hall (1967), Combinatorial Theory, Blaisde11, Waltham, Massachusetts.
[6] C.L.Liu, (1968) ,Introduction to Combinatorial Mathematics, McGraw-Hi11, New York.
[7] John Riordan, ( 1 980) , An Introduction to Combinatorial Analysis, Princeton University Press,Princeton,New Jersey. |
| Description: | 碩士
國立政治大學
應用數學系
83751010 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#B2002002893 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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