一個珠狀排列的公式

Abstract

這篇論文的目的，是要推廣學長的論文《一個環狀排列的公式》，欲藉由波利亞計數方法，來建立一個可計算任何珠狀排列問題的公式。為了達到這個目的，需要對循環群的概念及正n邊形群的結構做些介紹；並且說明伯恩賽定理及波利亞計數方法的內容；最後，利用波利亞計數定理，整理出珠狀排列的公式，並舉出實例，以顯示其實用價值。

The purpose of this thesis is to expand the conclusion of the thesis ”A Formula for Calculating Circular Permutations”, we want to establish a formula that can calculate any type of the necklace permutations by the Pólya’ s enumeration method . Firstly , we introduce the concept of the cyclic groups , and discuss the structure of the dihedral group . Secondly , we illustrate the Burnside theorem , and the Pólya’ s enumeration method . Finally , we conclude the formula for calculating necklace permutations . And we also give several examples to reveal the results .