| dc.contributor.advisor | 張宜武 | zh_TW |
| dc.contributor.author (Authors) | 王佑欣 | zh_TW |
| dc.contributor.author (Authors) | Yuhsin Wang | en_US |
| dc.creator (作者) | 王佑欣 | zh_TW |
| dc.creator (作者) | Yuhsin Wang | en_US |
| dc.date (日期) | 2002 | en_US |
| dc.date.accessioned | 17-Sep-2009 13:44:52 (UTC+8) | - |
| dc.date.available | 17-Sep-2009 13:44:52 (UTC+8) | - |
| dc.date.issued (上傳時間) | 17-Sep-2009 13:44:52 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0089751011 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/32558 | - |
| 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) | 89751011 | zh_TW |
| dc.description (描述) | 91 | zh_TW |
| dc.description.abstract (摘要) | 在這篇論文裡，我們將要討論一類古典的問題，這類問題已經經由許多方法解決，例如：遞迴關係式、差分方程式、尤拉公式等等。接著我們歸納低維度的特性，並藉由定義出一組方程式-標準n維空間分割系統-來推廣這些特性到一般的$n$維度空間中。然後我們利用演算法來提供一個更直接的組合論證法。最後，我們會把問題再細分成有界區域與無界區域的個數。 | zh_TW |
| dc.description.abstract (摘要) | In this article, we will discuss a class of classical questions had been solved by Recurrence Relation, Difference Equation, and Euler`s Formula, etc.. And then, we construct a system of equations -Standard Partition System of n-Dimensional Space- to generalize the properties of maximizing the number of regions made up by k partitioner in an n-dimensional space and look into the construction of each dimension. Also, we provide a more directly Combinatorial Argument by Algorithm for this kind of question. At last, we focus on the number of bounded regions and unbounded regions in sense of maximizing the number of regions. | en_US |
| dc.description.tableofcontents | Abstract i中文摘要 ii1 Introduction 1 1.1 Introduction............................................1 1.2 Description of Three Original Questions.................22 Solved By Recurrence Relation 3 2.1 Solution by Recurrence Relation for Question 1..........3 2.2 Solution by Recurrence Relation for Question 2..........4 2.3 Solution by Recurrence Relation for Question 3..........63 General Question of Higher Dimensional Spaces 8 3.1 Generalizing These Three Classical Questions............8 3.2 The Properties of Point, Line, and 3-D Space............9 3.3 The Properties of General Question and Standard Partition System of n-Dimensional Space..........................10 3.4 Proof of the Properties................................11 3.5 Solution by Recurrence Relation for General Question...154 Solved By Combinatorial Argument 17 4.1 Non-isomorphic of k-Max-Line-Drawing and k-Max-Plane- Drawing................................................17 4.2 Combinatorial Argument with Algorithm..................19 4.3 Combinatorial Argument for Higher Dimensional Space with Algorithm..............................................21 4.4 Presentation of Partitions in the Lower Dimensional Space..................................................22 4.5 A List of All Numbers..................................255 Number of Bounded Regions 26 5.1 Number of Bounded Regions in Sense of k-max-point- drawing................................................26 5.2 Number of Bounded Regions in Sense of k-max-line- drawing................................................27 5.3 Number of Bounded Regions in Sense of k-max-plane- drawing................................................28 5.4 Number of Bounded Regions of Higher Dimensional Space..286 Number of Unbounded Regions 30 6.1 Number of Unbounded Regions in Sense of k-max-point- drawing................................................30 6.2 Number of Unbounded Regions in Sense of k-max-line- drawing................................................31 6.3 Number of Unbounded Regions in Sense of k-max-plane- drawing................................................31 6.4 Number of Unbounded Regions of Higher Dimensional Space..................................................32References 34 | zh_TW |
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| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.format.mimetype | application/pdf | - |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0089751011 | en_US |
| dc.subject (關鍵詞) | Recurrence Relation | en_US |
| dc.subject (關鍵詞) | Difference Equation | en_US |
| dc.subject (關鍵詞) | Euler`s Formula | en_US |
| dc.subject (關鍵詞) | Standard Partition System of n-Dimensional | en_US |
| dc.subject (關鍵詞) | Partitioner | en_US |
| dc.subject (關鍵詞) | n-dimensional space | en_US |
| dc.subject (關鍵詞) | Combinatorial Argument | en_US |
| dc.subject (關鍵詞) | Algorithm | en_US |
| dc.subject (關鍵詞) | Bounded Region | en_US |
| dc.subject (關鍵詞) | Unbounded Region | en_US |
| dc.title (題名) | Combinatorial Argument of Partition with Point, Line, and Space | zh_TW |
| dc.title (題名) | 點線面與空間分割的組合論證法 | zh_TW |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | [1] Alan Tucker, Applied Combinatorics, 3rd ed., John Wiley & | zh_TW |
| dc.relation.reference (參考文獻) | Sons, New York, 1995, 281-282, 305. | zh_TW |
| dc.relation.reference (參考文獻) | [2] 簡蒼調, 續談觀察歸納法價值, 數學傳播, 第2卷第1期, 頁33-37. | zh_TW |
| dc.relation.reference (參考文獻) | [3] 何景國, 差分法及其在組合學上的應用, 數學傳播, 第10卷第1期, | zh_TW |
| dc.relation.reference (參考文獻) | 頁49-51. | zh_TW |
| dc.relation.reference (參考文獻) | [4] 宋秉信, 從尤拉公式到空間的平面分割, 數學傳播, 第22卷第3期, | zh_TW |
| dc.relation.reference (參考文獻) | 頁54-60. | zh_TW |
| dc.relation.reference (參考文獻) | [5] Alan Tucker, Applied Combinatorics, 3rd ed., John Wiley & | zh_TW |
| dc.relation.reference (參考文獻) | Sons, New York, 1995, 216-218. | zh_TW |
| dc.relation.reference (參考文獻) | [6] Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. | zh_TW |
| dc.relation.reference (參考文獻) | Spence, Linear Algebra, 3rd ed., Prentice-Hall, 1997, 47-48. | zh_TW |
