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Computation of the Number of Score Sequences in Round-Robin Tournaments

Published online by Cambridge University Press:  20 November 2018

T.V. Narayana  and
D.H. Bent
T.V. Narayana
Affiliation:
University of Alberta, Edmonton, Alberta
D.H. Bent
Affiliation:
University of Alberta, Edmonton, Alberta
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We consider round-robin tournaments of n players in which, at each encounter, the winner is awarded 1 point and the loser 0 (ties are excluded).

Let

1

be the n scores, ordered in a non-decreasing sequence. Clearly

2

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 1 , March 1964 , pp. 133 - 136
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. David, H. A., Tournaments and Paired Comparisons. Biometrika, Vol. 46, Parts I and II, 139–149.Google Scholar
2. Landau, H. G., On dominance relations, and the structure of animal societies, III. The condition for a score structure. Bull. Math. Biophysics, 15(1963), 143–148.Google Scholar
3. Moon, J. W., On the score sequence of an N-Partite Tournament. Canad. Math. Bull., Vol. 5, No. 1, Jan. 1962, 51–58.Google Scholar
4. Moon, J. W. and Moser, L., Almost all Tournaments are Irreducible. Canad. Math. Bull., Vol. 5, No. 1, Jan. 1962, 61–65.Google Scholar