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    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: 2017-08-10 09:57:57 (UTC+8)
    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
    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.
    參考文獻: 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 Fortieth
    Southeastern 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 binomial
    coefficients 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 number
    related 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
    顯示於類別:[應用數學系] 學位論文

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