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Ringing the changes

Published online by Cambridge University Press:  24 October 2008

Arthur T. White
Arthur T. White
Affiliation:
Western Michigan University, Kalamazoo, Michigan
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Abstract

The ancient and continuing art of change ringing, or campanology (how the British ring church bells), is studied from a mathematical viewpoint. An extent on n bells is regarded as a hamiltonian cycle in a Cayley colour graph for the symmetric group Sn, embedded on an appropriate surface. Two methods for variable n (Plain Bob for all n and Grandsire for n =; 3 (mod 4)) are discussed, and a new method for n odd is introduced. All minimus methods (n = 4) and five doubles methods (n = 5) are depicted, one of these being the new No Call Doubles.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 2 , September 1983 , pp. 203 - 215
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

(1)Budden, F. J.The Fascination of groups (Cambridge University Press, 1972).Google Scholar
(2)Camp, J.Discovering bells and bellringing (Shire, Aylesbury, 1975).Google Scholar
(3)Coxeter, H. S. M. and Moser, W. O.Generators and relations for discrete groups (Springer-Verlag, New York, 1965).Google Scholar
(4)Dickinson, D. J.On Fletcher's paper Campanological groups. Amer. Math. Monthly 64 (1957), 331332.Google Scholar
(5)Fletcher, T. J.Campanological groups. Amer. Math. Monthly 63 (1956), 619626.CrossRefGoogle Scholar
(6)Price, B. D.Mathematical groups in campanology. Math. Gaz. 53 (1969), 129133.CrossRefGoogle Scholar
(7)Rankin, R. A.A campanological problem in group theory. Math. Proc. Cambridge Philos. Soc. 44 (1948), 1725.Google Scholar
(8)Rapaport, E. S.Cayley colour groups and Hamilton lines. Scripta Math. 24 (1959), 5158.Google Scholar
(9)Sayers, D. L.The nine tailors (Victor Gollancz, London, 1934).Google Scholar
(10)Snowdon, J. and Snowdon, W.Diagrams (Jasper Snowdon Change Ringing Series, C. Groome, Kettering, 1972).Google Scholar
(11)White, A. T. Graphs of groups on surfaces. Combinatorial Surveys: Proceedings of the Sixth British Combinatorial Conference, ed. Cameron, P. J. (Academic Press, London, 1977), pp. 165197.Google Scholar
(12)Wilson, W. G.Change ringing (Faber, London, 1965).Google Scholar