Application Characteristics Analysis of Polya Count Theorems

摘要

Polya count is a method which can solve a special kind of counting problems based on the theory of permutation group, and the count has been widely used in the calculation scientific field. Polya count process can be abstractly described as coloring, classification and counting of graphics, and it requires deep understanding of the real problem, such as the factors of the number of colors, topology, requirement, etc. In this paper, three existing Polya count theorems are expatiated, and their intrinsic relationship and application characteristics are discussed. Guidance and inspiration are provided to solve the practical Polya count application problems.