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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Fan Rong K. Chung, On the Ramsey Numbers N(3,...,3;2), Discrete Math. 5 (1973), 317–321.
J.H. Conway, A group of order 8, 315, 553, 613, 086, 720, 000. Bull. London Math. Soc. 1 (1969), 79–86.
Jon Folkman, Notes on the Ramsey number N(3,3,3,3), Manuscript, Rand Corporation, Santa Monica, California, 1967.
Branko Grünbaum and G.C. Shephard, Tilings by regular polygons, Math. Mag. 50 (1977), 227–247.
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).
K. Heinrich, Proper 3-colourings of K6, Ars Combinatoria 1 (1976), 191–213.
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).
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).
John Leech, Some sphere packings in higher space, Canad. J. Math. 16 (1964), 657–682.
John Leech, Notes on sphere packings, Canad. J. Math. 19 (1977), 251–267.
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).
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).
Sheila Oates Macdonald and Anne Penfold Street, The seven friezes and how to colour them, Utilitas Math. 13 (1978), 271–292.
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).
F.J. McWilliams, Prmutation decoding of systematic codes, Bell System Tech. J. 43 (1964), 485–505.
F.J. McWilliams and N.J.A. Sloane, The theory of error-correcting codes, (North-Holland, Amsterdam, New York, Oxford, 1977).
Richard L. Roth, Colour symmetry and group theory (preprint, 1978).
Anne Penfold Street, A maximal sum-free set in A5, Utilitas Math. 5 (1974), 85–91.
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).
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).
Earl Glen Whitehead, Jr. The Ramsey number N(3,...,3;2), Discrete Math. 4 (1973), 389–396.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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
