Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/111782| 題名: | 一個卡特蘭等式的組合證明 A Combinatorial Proof of a Catalan Identity |
作者: | 劉映君 | 貢獻者: | 李陽明 劉映君 |
關鍵詞: | 卡特蘭等式 Catalan Identity |
日期: | 2017 | 上傳時間: | 10-八月-2017 | 摘要: | 在這篇論文裡，我們探討卡塔蘭等式 (n + 2)Cn+1 = (4n + 2)C2 的證明\n方法。以往都是用計算的方式來呈現卡塔蘭等式的由來，但我們選擇用組合\n的方法來證明卡塔蘭等式。\n這篇論文主要是應用 Cn+1 壞路徑對應到打點 Cn 好路徑以及 Cn+1 好路\n徑對應到打點 Cn 壞路徑的⽅式來證明卡特蘭等式。 In this thesis, we give another approach to prove Catalan identity,\n(n + 2)Cn+1 = (4n + 2)C2. In the past we use the method of computation to show Catalan Identity, in this thesis we choose a combinatorial proof of the Catalan identity.\nThis thesis is primary using the functions from Cn+1 totally bad path to Cn dotted good path, and from Cn+1 good path to Cn dotted totally bad path. |
參考文獻: | Ronald Alter. Some remarks and results on Catalan numbers. pages 109–132, 1971.\n[2] Ronald Alter and K. K. Kubota. Prime and prime power divisibility of Catalan numbers.\nJ. Combinatorial Theory Ser. A, 15:243–256, 1973.\n[3] Federico Ardila. Catalan numbers. Math. Intelligencer, 38(2):4–5, 2016.\n[4] Young-Ming Chen. The Chung-Feller theorem revisited. Discrete Math., 308(7):1328–\n1329, 2008.\n[5] Ömer E ̆gecioğlu. A Catalan-Hankel determinant evaluation. In Proceedings of the Fortieth\nSoutheastern International Conference on Combinatorics, Graph Theory and Computing,\nvolume 195, pages 49–63, 2009.\n[6] R. Johnsonbaugh. Discrete Mathematics. Pearson/Prentice Hall, 2009.\n[7] Thomas Koshy. Catalan numbers with applications. Oxford University Press, Oxford,\n2009.\n[8] Tamás Lengyel. On divisibility properties of some differences of the central binomial\ncoefficients and Catalan numbers. Integers, 13:Paper No. A10, 20, 2013.\n[9] Youngja Park and Sangwook Kim. Chung-Feller property of Schröder objects. Electron.\nJ. Combin., 23(2):Paper 2.34, 14, 2016.\n[10] Matej ̌Crepin ̌sek and Luka Mernik. An efficient representation for solving Catalan number\nrelated problems. Int. J. Pure Appl. Math., 56(4):589–604, 2009. | 描述: | 碩士 國立政治大學 應用數學系 103751014 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0103751014 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| 101401.pdf | 1.05 MB | Adobe PDF2 | View/Open |
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.