On the Pólya Enumeration Theorem
DOI: 10.4236/iim.2009.13025   PDF    HTML     9,646 Downloads   14,298 Views   Citations


Simple formulas for the number of different cyclic and dihedral necklaces containing nj beads of the j-th color, and , are derived, using the Pólya enumeration theorem.

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FEL, L. (2009) On the Pólya Enumeration Theorem. Intelligent Information Management, 1, 172-173. doi: 10.4236/iim.2009.13025.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] G. Pólya, “Kombinatorische anzahlbestimmungen für Gruppen, Graphen, und chemische Verbindungen,” Acta Math., Vol. 68, pp. 145–254, 1937.
[2] F. Harary and E. M. Palmer, “Graphical enumeration,” Academic Press, New York, 1973.
[3] J. J. Rotman, “An introduction to the theory of groups,” Boston, Mass., Allyn and Bacon, Chapter 3, 1984.
[4] G. Polya and R. C. Read, “Combinatorial enumeration of groups, graphs, and chemical compounds,” Springer, New York, 1987.
[5] F. Harary, “Graph theory,” Reading, Addison-Wesley, MA, 1994.
[6] A. Kerber, “Applied finite group actions,” 2nd Ed., Springer, Berlin, Chap. 3, 1999.

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