| dc.contributor.advisor | 李陽明 | zh_TW |
| dc.contributor.author (Authors) | 涂健晏 | zh_TW |
| dc.creator (作者) | 涂健晏 | zh_TW |
| dc.date (日期) | 2014 | en_US |
| dc.date.accessioned | 3-Feb-2015 15:00:41 (UTC+8) | - |
| dc.date.available | 3-Feb-2015 15:00:41 (UTC+8) | - |
| dc.date.issued (上傳時間) | 3-Feb-2015 15:00:41 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G1017510011 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/73347 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 101751001 | zh_TW |
| dc.description (描述) | 103 | zh_TW |
| dc.description.abstract (摘要) | 在本篇論文，我們討論兩個組合等式，先利用整數分割及生成函數來證明，再給一個簡潔的方式證明這些整數分割之間的對應;第一章我們先對生成函數、整數分割、2的冪分割以及相異項與奇項分割作一個簡單的介紹，第二章說明並證明2的奇冪分割和偶冪分割的對射，第三章說明並證明相異項與奇項分割的對射。 | zh_TW |
| dc.description.tableofcontents | 口試委員會審定書.............................. i致謝........................................ ii中文摘要..................................... iiiAbstract ....................................iv目錄..........................................v第一章序論.................................... 1第一節生成函數................................. 1第二節整數分割................................. 5第三節2 的冪分割............................... 7第四節相異項與奇項分割.......................... 10第二章(1-x)g*(x)=1 的對射證明............... 12第一節2 的冪分割的對射證明....................... 12第三章 IIk>=1(1+x^k)=IIk>=1\\(1-x^(2k-1)) 的對射證明..... 17第一節相異項與奇項分割的對射證明................... 17第四章展望..................................... 24第一節更多關於整數分割的探討...................... 24參考文獻....................................... 25 | zh_TW |
| dc.format.extent | 389481 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G1017510011 | en_US |
| dc.subject (關鍵詞) | 整數分割 | zh_TW |
| dc.title (題名) | 有關整數分割的對射證明 | zh_TW |
| dc.title (題名) | About Bijective Proofs of Integer Partitions | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | [1] National Institute for Compilation and Translation. http://terms.naer.edu.tw/.[2] George E. Andrews. Number theory. New York : Dover Publications, 1938.[3] George E. Andrews. The theory of partitions. London ; Reading, Mass. : Addison-WesleyPub. Co., Advanced Book Program, 1976.[4] G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers. OxfordUniv.Press, London and New York., 1960.[5] D. R. Hickerson. Identities relating the number of partitions into an even and odd numberof parts. J. Combinatorial Theory A15, 1973.[6] D. R. Hickerson. A partition identity of Euler type. Amer. Math. Monthly 81, 1974.[7] Chung Laung Liu. Introduction to combinatorial mathematics. McGraw-Hill, 1968.[8] Fred S. Roberts ; Barry Tesman. Applied combinatorics. Upper Sadle River, N.J. : Prentice-Hall, 2005.[9] Alan Tucker. Applied combinatorics. Hoboken, N.J. : John Wiley and Sons, 2012. | zh_TW |
