Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral Groups
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 algorith...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/176598 |
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| author | Dakun Zhang Yonggang Lin Guozhi Song |
| author_facet | Dakun Zhang Yonggang Lin Guozhi Song |
| author_sort | Dakun Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-dad502737b4e4b2dbde2247278ef8a5a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-dad502737b4e4b2dbde2247278ef8a5a2025-02-03T00:59:19ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/176598176598Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral GroupsDakun Zhang0Yonggang Lin1Guozhi Song2School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin 300160, ChinaSchool of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, ChinaSchool of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin 300160, ChinaThe 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.http://dx.doi.org/10.1155/2013/176598 |
| spellingShingle | Dakun Zhang Yonggang Lin Guozhi Song Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral Groups Abstract and Applied Analysis |
| title | Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral Groups |
| title_full | Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral Groups |
| title_fullStr | Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral Groups |
| title_full_unstemmed | Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral Groups |
| title_short | Classification Formula and Generation Algorithm of Cycle Decomposition Expression for Dihedral Groups |
| title_sort | classification formula and generation algorithm of cycle decomposition expression for dihedral groups |
| url | http://dx.doi.org/10.1155/2013/176598 |
| work_keys_str_mv | AT dakunzhang classificationformulaandgenerationalgorithmofcycledecompositionexpressionfordihedralgroups AT yongganglin classificationformulaandgenerationalgorithmofcycledecompositionexpressionfordihedralgroups AT guozhisong classificationformulaandgenerationalgorithmofcycledecompositionexpressionfordihedralgroups |