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Abstract and Applied Analysis
Volume 2013, Article ID 176598, 6 pages
Research Article

Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral Groups

1School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin 300160, China
2School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Received 17 September 2012; Accepted 5 December 2012

Academic Editor: Zengqin Zhao

Copyright © 2013 Dakun Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The necessary of classification research on common formula of group (dihedral group) cycle decomposition expression is illustrated. It includes the reflection and rotation conversion, which derived six common formulae on cycle decomposition expressions of group; it designed the generation algorithm on the cycle decomposition expressions of group, which is based on the method of replacement conversion and the classification formula; algorithm analysis and the results of the process show that the generation algorithm which is based on the classification formula is outperformed by the general algorithm which is based on replacement conversion; it has great significance to solve the enumeration of the necklace combinational scheme, especially the structural problems of combinational scheme, by using group theory and computer.