政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/18846
English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  全文筆數/總筆數 : 113451/144438 (79%)
造訪人次 : 51244039      線上人數 : 929
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
搜尋範圍 查詢小技巧：
  • 您可在西文檢索詞彙前後加上"雙引號"，以獲取較精準的檢索結果
  • 若欲以作者姓名搜尋，建議至進階搜尋限定作者欄位，可獲得較完整資料
    •  進階搜尋
    政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 >  Item 140.119/18846


    請使用永久網址來引用或連結此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/18846


    題名: The Chung-Feller Theorem Revisited
    作者: 李陽明
    Chen, Young-Ming
    貢獻者: 應數系
    關鍵詞: Dyck paths;Catalan numbers
    日期: 2008-04
    上傳時間: 2008-12-24 13:39:20 (UTC+8)
    摘要: Dyck paths are the most investigated objects related to the Catalan numbers Cn (see [2], [6], [5] and [8]). An n-Dyck path with k flaws is a path from (0,0) to (2n,0) with up (1,1) and down (1,-1) steps having k down steps below the x-axis. Surprisingly, the number of n-Dyck paths with k flaws is independent of k which is the Chung–Feller theorem. In [1], the famous theorem was first proved by means of analytic method. The theorem was subsequently treated by more combinatorial methods in [7] (using cyclic permutation) and in [4] (using the Taylor expansions of generating functions). Recently, Eu et al. [3] proved a refinement of this result. In this note, our purpose is to provide a direct and elegant bijective proof of Chung–Feller theorem. We utilize a simple bijection between n-Dyck paths with k flaws and n-Dyck paths with k+1 flaws for k=0,1,…,n-1 to yield this result (Theorem 0.1).
    關聯: Discrete Mathematics, 308(7), 1328-1329
    資料類型: article
    DOI 連結: http://dx.doi.org/http://dx.doi.org/10.1016/j.disc.2007.03.068
    DOI: 10.1016/j.disc.2007.03.068
    顯示於類別:[應用數學系] 期刊論文

    文件中的檔案:

    檔案 描述 大小格式瀏覽次數
    1328-1329.pdf123KbAdobe PDF21156檢視/開啟


    在政大典藏中所有的資料項目都受到原著作權保護.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - 回饋