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Title: Combinatorial Argument of Partition with Point, Line, and Space
Authors: 王佑欣
Yuhsin Wang
Contributors: 張宜武
Yuhsin Wang
Keywords: Recurrence Relation
Difference Equation
Euler's Formula
Standard Partition System of n-Dimensional
n-dimensional space
Combinatorial Argument
Bounded Region
Unbounded Region
Date: 2002
Issue Date: 2009-09-17 13:44:52 (UTC+8)
Abstract: 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。
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.
Reference: [1] Alan Tucker, Applied Combinatorics, 3rd ed., John Wiley &
Sons, New York, 1995, 281-282, 305.
[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.
[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,
[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,
[5] Alan Tucker, Applied Combinatorics, 3rd ed., John Wiley &
Sons, New York, 1995, 216-218.
[6] Stephen H. Friedberg, Arnold J. Insel, and Lawrence E.
Spence, Linear Algebra, 3rd ed., Prentice-Hall, 1997, 47-48.
Description: 碩士
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Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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