×

Classification formula and generation algorithm of cycle decomposition expression for dihedral groups. (English) Zbl 1272.68478

MSC:

68W30 Symbolic computation and algebraic computation
20D60 Arithmetic and combinatorial problems involving abstract finite groups
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Hu, G. Z., The Application of Modern Algebra (1992), Beijing, China: Tsinghua University Press, Beijing, China
[2] Shinoda, K.; Yamada, M., A family of Hadamard matrices of dihedral group type, Discrete Applied Mathematics, 102, 1-2, 141-150 (2000) · Zbl 0943.05026 · doi:10.1016/S0166-218X(99)00235-8
[3] Renault, G., Computation of the splitting field of a dihedral polynomial, Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC ’06) · Zbl 1356.12014
[4] Song, S.; Wang, D., Reliability analysis of the Cayley graphs of dihedral groups, Tsinghua Science and Technology, 16, 1, 36-40 (2011) · Zbl 1265.05299 · doi:10.1016/S1007-0214(11)70006-2
[5] Uno Miyuki; Kano, M., Visual cryptography schemes with dihedral group access structure for many images, Proceedings of the 3rd International Conference on Information Security Practice and Experience (ISPEC ’07)
[6] Lange, H.; Recillas, S., Abelian varieties with group action, Journal fur die Reine und Angewandte Mathematik, 575, 135-155 (2004) · Zbl 1072.14053
[7] Bucikiewicz, S.; Dȩbski, L.; Florek, W., Application of algebraic combinatorics to finite spin systems with dihedral symmetry, Acta Physica Polonica A, 100, 4, 453-475 (2001)
[8] Ecker, J., Affine completeness of generalised dihedral groups, Canadian Mathematical Bulletin, 49, 3, 347-357 (2006) · Zbl 1112.20018 · doi:10.4153/CMB-2006-035-8
[9] Leung, K. H.; Schmidt, B., Asymptotic nonexistence of difference sets in dihedral groups, Journal of Combinatorial Theory A, 99, 2, 261-280 (2002) · Zbl 1002.05006 · doi:10.1006/jcta.2002.3269
[10] Xu, B. G., On the formulas of enumeration in necklace problem, Journal of East China Jiaotong University, 20, 5, 113-114 (2003)
[11] Wang, Z. M., The application of group index in combinatorial calculating, Journal of Tangshang Teachers College, 23, 1, 9-10 (2001)
[12] Zhang, D. K.; Wang, G. X., Construction of three-dimensional model of platonic solid coloring mode based on group theory, Ruan Jian Xue Bao/Journal of Software, 15, 2, 292-299 (2004) · Zbl 1107.68508
[13] Fu, X. Q.; Wang, X. D., Algorithm and Datastruct (2000), Beijing, China: Publishing House of Electronics Industry, Beijing, China
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.