Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/73347| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 李陽明 | zh_TW |
| dc.contributor.author | 涂健晏 | zh_TW |
| dc.creator | 涂健晏 | zh_TW |
| dc.date | 2014 | en_US |
| dc.date.accessioned | 2015-02-03T07:00:41Z | - |
| dc.date.available | 2015-02-03T07:00:41Z | - |
| dc.date.issued | 2015-02-03T07:00:41Z | - |
| dc.identifier | G1017510011 | en_US |
| dc.identifier.uri | http://nccur.lib.nccu.edu.tw/handle/140.119/73347 | - |
| dc.description | 碩士 | zh_TW |
| dc.description | 國立政治大學 | zh_TW |
| dc.description | 應用數學研究所 | zh_TW |
| dc.description | 101751001 | zh_TW |
| dc.description | 103 | zh_TW |
| dc.description.abstract | 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\n致謝........................................ ii\n中文摘要..................................... iii\nAbstract ....................................iv\n目錄..........................................v\n第一章序論.................................... 1\n第一節生成函數................................. 1\n第二節整數分割................................. 5\n第三節2 的冪分割............................... 7\n第四節相異項與奇項分割.......................... 10\n第二章(1-x)g*(x)=1 的對射證明............... 12\n第一節2 的冪分割的對射證明....................... 12\n第三章 IIk>=1(1+x^k)=IIk>=1\\(1-x^(2k-1)) 的對射證明..... 17\n第一節相異項與奇項分割的對射證明................... 17\n第四章展望..................................... 24\n第一節更多關於整數分割的探討...................... 24\n參考文獻....................................... 25 | zh_TW |
| dc.format.extent | 389481 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri | http://thesis.lib.nccu.edu.tw/record/#G1017510011 | en_US |
| dc.subject | 整數分割 | zh_TW |
| dc.title | 有關整數分割的對射證明 | zh_TW |
| dc.title | About Bijective Proofs of Integer Partitions | en_US |
| dc.type | thesis | en |
| dc.relation.reference | [1] National Institute for Compilation and Translation. http://terms.naer.edu.tw/.\n[2] George E. Andrews. Number theory. New York : Dover Publications, 1938.\n[3] George E. Andrews. The theory of partitions. London ; Reading, Mass. : Addison-Wesley\nPub. Co., Advanced Book Program, 1976.\n[4] G. H. Hardy and E. M. Wright. An Introduction to the Theory of Numbers. Oxford\nUniv.Press, London and New York., 1960.\n[5] D. R. Hickerson. Identities relating the number of partitions into an even and odd number\nof parts. J. Combinatorial Theory A15, 1973.\n[6] D. R. Hickerson. A partition identity of Euler type. Amer. Math. Monthly 81, 1974.\n[7] Chung Laung Liu. Introduction to combinatorial mathematics. McGraw-Hill, 1968.\n[8] Fred S. Roberts ; Barry Tesman. Applied combinatorics. Upper Sadle River, N.J. : Prentice-\nHall, 2005.\n[9] Alan Tucker. Applied combinatorics. Hoboken, N.J. : John Wiley and Sons, 2012. | zh_TW |
| item.openairetype | thesis | - |
| item.cerifentitytype | Publications | - |
| item.grantfulltext | restricted | - |
| item.fulltext | With Fulltext | - |
| item.openairecristype | http://purl.org/coar/resource_type/c_46ec | - |
| Appears in Collections: | 學位論文 | |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| 001101.pdf | 380.35 kB | Adobe PDF2 | View/Open |
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