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研究生： 陳瑞祥
Chen, Jui-Hsiang
論文名稱： 和卡特蘭數及Fine數有關的兩種特殊型停車函數
Two Special Types of Parking Functions Related to Catalan Number and Fine Number
指導教授： 黃柏嶧
Huang, Po-Yi
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年： 2019
畢業學年度： 107
語文別： 英文
論文頁數： 21
中文關鍵詞： 停車函數 、卡特蘭數 、Fine數 、卡特蘭三角的對角和
外文關鍵詞： parking function, Catalan number, Fine number, diagonal sums of Catalan triangle
相關次數： 點閱：165  下載：8 
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    • 我們從單峰數列得到研究靈感，藉由討論兩種特殊的停車函數：V-停車函數和Lambda-停車函數，我們證明了驚人的事實：V-停車函數的數量就是卡特蘭數，以及Lambda-停車函數的數量就是Fine數。(在附錄A中，我們以組合證明的方式，驗證了卡特蘭三角的對角和是Fine數。)

    We introduce two special types of parking function, V-parking function and Lambda-parking function, which are inspired by the unimodal sequence.
    Then, we prove the suprising facts that the number of V-parking functions are Catalan numbers and the number of Lambda-parking functions are Fine numbers. (In appendix A, we verify that the diagonal sums of Catalan triangle are Fine numbers by giving bijections.)

    摘要 I Abstract II 誌謝 III List of Tables VI List of Figures VII 1 Introduction 1 2 How many V-parking functions? 4 3 How many Λ-parking functions? 8 References 13 A A combinatorial proof about the diagonal sums of Catalan triangle 14 B Stories and programmings 16 B.1 Programming for Λn ....16 B.2 Programming for Λn,i ......20

    [1] Deutsch, E., & Shapiro, L. A survey of the Fine numbers. Discrete Mathematics, 241(1-3), 241-265. (2001).
    [2] Shapiro, L. W. A Catalan triangle. Discrete Mathematics, 14(1), 83-90. (1976).
    [3] Stanley, R.P. Enumerative Combinatorics (2nd ed., Vol. 1). Retrieved from http://www-math.mit.edu/~rstan/ec/ec1.pdf. (2011).
    [4] Stanley, R.P. Enumerative Combinatorics (Vol. 2). Cambridge University Press. New York. (1999).
    [5] Yan, C.H. Parking Functions. In Bóna, M. (Ed.), Handbook of enumerative combinatorics. CRC Press. Boca Raton. (pp. 835-893). (2015).

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