Skip to main content

Combinatorics — A branch of group theory?

Invited Addresses

  • 504 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 748)

Abstract

After a brief survey of the interaction between combinatorics and group theory, three illustrations of the application of group theory to combinatorial problems are given.

Keywords

  • Automorphism Group
  • Simple Group
  • Cayley Graph
  • Code Word
  • Edge Colouring

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fan Rong K. Chung, On the Ramsey Numbers N(3,...,3;2), Discrete Math. 5 (1973), 317–321.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. J.H. Conway, A group of order 8, 315, 553, 613, 086, 720, 000. Bull. London Math. Soc. 1 (1969), 79–86.

    CrossRef  MathSciNet  Google Scholar 

  3. Jon Folkman, Notes on the Ramsey number N(3,3,3,3), Manuscript, Rand Corporation, Santa Monica, California, 1967.

    MATH  Google Scholar 

  4. Branko Grünbaum and G.C. Shephard, Tilings by regular polygons, Math. Mag. 50 (1977), 227–247.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Branko Grünbaum and G.C. Shephard, Incidence symbols and their applications, Proc. Symposium on relations between Combinatorics and other parts of Mathematics, Columbus, Ohio, 1978 (to appear).

    Google Scholar 

  6. K. Heinrich, Proper 3-colourings of K6, Ars Combinatoria 1 (1976), 191–213.

    MathSciNet  MATH  Google Scholar 

  7. K. Heinrich, A non-imbeddable proper colouring, Combinatorial Mathematics IV, Proc. Fourth Australian Conf. Lecture Notes in Math. 560, 93–115, (Springer-Verlag, Berlin, Heidelberg, New York, 1976).

    CrossRef  Google Scholar 

  8. Wilfred Imrich, Subgroup theorems and graphs, Combinatorial Mathematics V, Proc. Fifth Australian Conf. Lecture Notes in Math. 622, 1–27, (Springer-Verlag, Berlin, Heidelberg, New York, 1977).

    CrossRef  Google Scholar 

  9. John Leech, Some sphere packings in higher space, Canad. J. Math. 16 (1964), 657–682.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. John Leech, Notes on sphere packings, Canad. J. Math. 19 (1977), 251–267.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Sheila Oates Macdonald, Sum-free sets in loops, Combinatorial Mathematics V, Proc. Fifth Australian Conf. Lecture Notes in Math. 622, 141–147, (Springer-Verlag, Berlin, Heidelberg, New York, 1977).

    CrossRef  Google Scholar 

  12. Sheila Oates Macdonald and Anne Penfold Street, On crystallographic colour groups, Combinatorial Mathematics IV, Proc. Fourth Australian Conf. Lecture Notes in Math. 560, 149–157, (Springer-Verlag, Berlin, Heidelberg, New York, 1976).

    CrossRef  Google Scholar 

  13. Sheila Oates Macdonald and Anne Penfold Street, The seven friezes and how to colour them, Utilitas Math. 13 (1978), 271–292.

    MathSciNet  MATH  Google Scholar 

  14. Sheila Oates Macdonald and Anne Penfold Street, The analysis of colour symmetry, Combinatorial Mathematics VI, Proc. International Conf. (Canberra 1977), Lecture Notes in Math. (Springer-Verlag, Berlin, Heidelberg, New York, to appear).

    Google Scholar 

  15. F.J. McWilliams, Prmutation decoding of systematic codes, Bell System Tech. J. 43 (1964), 485–505.

    CrossRef  Google Scholar 

  16. F.J. McWilliams and N.J.A. Sloane, The theory of error-correcting codes, (North-Holland, Amsterdam, New York, Oxford, 1977).

    Google Scholar 

  17. Richard L. Roth, Colour symmetry and group theory (preprint, 1978).

    Google Scholar 

  18. Anne Penfold Street, A maximal sum-free set in A5, Utilitas Math. 5 (1974), 85–91.

    MathSciNet  MATH  Google Scholar 

  19. Anne Penfold Street, Embedding proper colourings, Combinatorial Mathematics IV, Proc. Fourth Australian Conf. Lecture Notes in Math. 560, 240–245, (Springer-Verlag, Berlin, Heidelberg, New York, 1976).

    CrossRef  Google Scholar 

  20. W.D. Wallis, Anne Penfold Street and Jennifer Seberry Wallis, Combinatorics: Room squares, sum-free sets and Hadamard matrices. Lecture Notes in Math. 292, (Springer-Verlag, Berlin, Heidelberg, New York, 1972).

    CrossRef  Google Scholar 

  21. Earl Glen Whitehead, Jr. The Ramsey number N(3,...,3;2), Discrete Math. 4 (1973), 389–396.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1979 Springer-Verlag

About this paper

Cite this paper

MacDonald, S.O. (1979). Combinatorics — A branch of group theory?. In: Horadam, A.F., Wallis, W.D. (eds) Combinatorial Mathematics VI. Lecture Notes in Mathematics, vol 748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102680

Download citation

  • DOI: https://doi.org/10.1007/BFb0102680

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09555-2

  • Online ISBN: 978-3-540-34857-3

  • eBook Packages: Springer Book Archive