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On the Pólya Enumeration Theorem

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DOI: 10.4236/iim.2009.13025    6,844 Downloads   10,483 Views   Citations
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ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

L. FEL, "On the Pólya Enumeration Theorem," Intelligent Information Management, Vol. 1 No. 3, 2009, pp. 172-173. doi: 10.4236/iim.2009.13025.

References

[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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