組合數學的主要目的之一就是要用簡單容易的方法來解決問題。在本篇論文中我們試著用組合的方法去證明以下的等式
ΣC<sup>2k</sup><sub>k</sub>C<sup>2t-2k</sup><sub>t-k</sub>=2<sup>2t</sup>
以往有人用生成函數的方法證出此式，在此我們提出一個不同的方法，希望對此式有一更清楚更深入的瞭解。首先我們先建構兩個集合，其個數各為ΣC<sup>2k</sup><sub>k</sub>C<sup>2t-2k</sup><sub>t-k</sub>和2<sup>2t</sup>。接著在這兩個集合之間，建立一個一對一且映成的函數來完成我們的證明。 / One of the main objective of combinatorial mathematics is to find an easy and simple way to solve problems. In this paper,we try to use a combinatorial method to prove the identity
ΣC<sup>2k</sup><sub>k</sub>C<sup>2t-2k</sup><sub>t-k</sub>=2<sup>2t</sup>
Its proof is known with generating functions. However, we present a different method, hoping to have a clear, and better understanding about this identity.
We construct two sets whose numbers of elements are, respectively,ΣC<sup>2k</sup><sub>k</sub>C<sup>2t-2k</sup><sub>t-k</sub> and 2<sup>2t</sup> and set up a bijective function, between the two sets to complete our proof.
| Identifer | oai:union.ndltd.org:CHENGCHI/B2002003904 |
| Creators | 劉麗珍, Liu, Li Jean |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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