The charm bracelet problem and its applications

  • Paul K. Stockmeyer
Part III: Contributed Papers New Results On Graphs And Combinatorics
Part of the Lecture Notes in Mathematics book series (LNM, volume 406)

Abstract

The necklace problem has proved to be both a sound pedagogical device in teaching enumeration theory and a valuable counting tool with several graphical applications. In this paper we solve the more general charm bracelet problem and provide two applications for which the necklace problem in not sufficient.

We set the stage in Section 1 by providing a brief review of the necklace problem. This serves as a basis for comparison in Section 2, where we discuss the charm bracelet problem and derive its solution. Sections 3 and 4 contain nontrivial graphical applications of the results of Section 2.

Definitions for all graphical terms and concepts can be found in [3]. For further background and broader treatment of topics of an enumerative nature, [5] should be consulted.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Burnside, W., Theory of Groups of Finite Order. Second Edition, Cambridge University Press, 1911. Reprinted Dover, 1955, New York.Google Scholar
  2. 2.
    Guy, R. K., "Dissecting a Polygon into Triangles", Research Report, University of Calgary, 1960.Google Scholar
  3. 3.
    Harary, F., Graph Theory. Addison-Wesley, 1969, Reading.Google Scholar
  4. 4.
    Harary, F., "Enumeration Under Group Action: Unsolved Graphical Enumeration Problems, IV." J. Comb. Theory, 8 (1970) 1–11.MATHCrossRefGoogle Scholar
  5. 5.
    Harary, F., and Palmer, E. M., Graphical Enumeration, Academic Press, 1973, New York.MATHGoogle Scholar
  6. 6.
    Harary, F., and Prins, G., "The Number of Homomorphically Irreducible Trees and Other Species", Acta Math. 101 (1959) 141–162.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Harary, F., Prins, G., Tutte, W. t., "The Number of Plane Trees", Indag. Math 26 (1964) 319–329.MathSciNetGoogle Scholar
  8. 8.
    Harary, F., and Robinson, R. W., "The Number of Achiral Trees", J. Reine Angew. Math., to appear.Google Scholar
  9. 9.
    Moon, J. W., and Moser, L., "Triangular Dissections of n-gons" Canad. Math. Bull. 6 (1963) 175–177.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Otter, R., "The Number of Trees", Ann. of Math. 49 (1948) 583–599.MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Pólya, G., "Kombinatorische Anzehlbestimmungen für Gruppen, Graphen und chemische Verbindungen", Acta Math. 68 (1937) 145–254.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin 1974

Authors and Affiliations

  • Paul K. Stockmeyer
    • 1
  1. 1.College of William and MaryUSA

Personalised recommendations