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The enumeration and bifurcations of ranking functions

Published online by Cambridge University Press:  17 April 2009

W.J. Walker
W.J. Walker
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand.
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Abstract

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Suppose n competitors each compete in r races and a ranking function F assigns a score F(j) to the competitor finishing in the jth position in each race. The sum of the scores over r races gives each competitor a final ranking. If n is fixed, the ranking function F bifurcates as r increases. The complete bifurcation behaviour is determined for n = 3 and some information obtained for n > 3.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 2 , April 1978 , pp. 287 - 292
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Thom, Ren´e, Structural stability and morphogenesis: an outline of a general theory of models (translated by Fowler, D.H.. Benjamin, Reading, Massachusetts; London; Amsterdam; Don Mills, Ontario; Sydney; Tokyo; 1975).Google Scholar
[2]Walker, W.J., “Algebraic and combinatorial results for ranking competitors in a sequence of races”, Discrete Math. 14 (1976), 297–304.CrossRefGoogle Scholar