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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 176598, 6 pages
http://dx.doi.org/10.1155/2013/176598
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.

Linked References

  1. G. Z. Hu, The Application of Modern Algebra, Tsinghua University Press, Beijing, China, 1992.
  2. K. Shinoda and M. Yamada, “A family of Hadamard matrices of dihedral group type,” Discrete Applied Mathematics, vol. 102, no. 1-2, pp. 141–150, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  3. G. Renault, “Computation of the splitting field of a dihedral polynomial,” in Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC '06), pp. 290–297, July 2006. View at Scopus
  4. S. Song and D. Wang, “Reliability analysis of the Cayley graphs of dihedral groups,” Tsinghua Science and Technology, vol. 16, no. 1, pp. 36–40, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. Uno Miyuki and M. Kano, “Visual cryptography schemes with dihedral group access structure for many images,” in Proceedings of the 3rd International Conference on Information Security Practice and Experience (ISPEC '07), vol. 4464, pp. 344–359, 2007.
  6. H. Lange and S. Recillas, “Abelian varieties with group action,” Journal fur die Reine und Angewandte Mathematik, no. 575, pp. 135–155, 2004. View at Zentralblatt MATH · View at Scopus
  7. S. Bucikiewicz, L. Dȩbski, and W. Florek, “Application of algebraic combinatorics to finite spin systems with dihedral symmetry,” Acta Physica Polonica A, vol. 100, no. 4, pp. 453–475, 2001. View at Scopus
  8. J. Ecker, “Affine completeness of generalised dihedral groups,” Canadian Mathematical Bulletin, vol. 49, no. 3, pp. 347–357, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. K. H. Leung and B. Schmidt, “Asymptotic nonexistence of difference sets in dihedral groups,” Journal of Combinatorial Theory A, vol. 99, no. 2, pp. 261–280, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  10. B. G. Xu, “On the formulas of enumeration in necklace problem,” Journal of East China Jiaotong University, vol. 20, no. 5, pp. 113–114, 2003 (Chinese).
  11. Z. M. Wang, “The application of group index in combinatorial calculating,” Journal of Tangshang Teachers College, vol. 23, no. 1, pp. 9–10, 2001 (Chinese).
  12. D. K. Zhang and G. X. Wang, “Construction of three-dimensional model of platonic solid coloring mode based on group theory,” Ruan Jian Xue Bao/Journal of Software, vol. 15, no. 2, pp. 292–299, 2004 (Chinese). View at Zentralblatt MATH · View at Scopus
  13. X. Q. Fu and X. D. Wang, Algorithm and Datastruct, Publishing House of Electronics Industry, Beijing, China, 2000.