Please use this identifier to cite or link to this item: `https://ah.nccu.edu.tw/handle/140.119/111782`

 Title: 一個卡特蘭等式的組合證明A Combinatorial Proof of a Catalan Identity Authors: 劉映君 Contributors: 李陽明劉映君 Keywords: 卡特蘭等式Catalan Identity Date: 2017 Issue Date: 2017-08-10 09:57:57 (UTC+8) Abstract: 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，但我們選擇用組合的方法來證明卡塔蘭等式。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 + 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.This 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. Reference: Ronald Alter. Some remarks and results on Catalan numbers. pages 109–132, 1971.[2] Ronald Alter and K. K. Kubota. Prime and prime power divisibility of Catalan numbers.J. Combinatorial Theory Ser. A, 15:243–256, 1973.[3] Federico Ardila. Catalan numbers. Math. Intelligencer, 38(2):4–5, 2016.[4] Young-Ming Chen. The Chung-Feller theorem revisited. Discrete Math., 308(7):1328–1329, 2008.[5] Ömer E ̆gecioğlu. A Catalan-Hankel determinant evaluation. In Proceedings of the FortiethSoutheastern International Conference on Combinatorics, Graph Theory and Computing,volume 195, pages 49–63, 2009.[6] R. Johnsonbaugh. Discrete Mathematics. Pearson/Prentice Hall, 2009.[7] Thomas Koshy. Catalan numbers with applications. Oxford University Press, Oxford,2009.[8] Tamás Lengyel. On divisibility properties of some differences of the central binomialcoefficients and Catalan numbers. Integers, 13:Paper No. A10, 20, 2013.[9] Youngja Park and Sangwook Kim. Chung-Feller property of Schröder objects. Electron.J. Combin., 23(2):Paper 2.34, 14, 2016.[10] Matej ̌Crepin ̌sek and Luka Mernik. An efficient representation for solving Catalan numberrelated problems. Int. J. Pure Appl. Math., 56(4):589–604, 2009. Description: 碩士國立政治大學應用數學系103751014 Source URI: http://thesis.lib.nccu.edu.tw/record/#G0103751014 Data Type: thesis Appears in Collections: [應用數學系] 學位論文

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