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Upsets in Round Robin Tournaments

Published online by Cambridge University Press:  20 November 2018

D. R. Fulkerson
D. R. Fulkerson*
Affiliation:
The RAND Corporation, Santa Monica, California, U.S.A.
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Consider a round robin tournament in which each of n players is required to play precisely one game with each other player, and assume that each game ends in a win or a loss. The results of such a tournament can be conveniently recorded in a square (0, 1)-matrix T = (tij) of order n by setting tij = 1 if player i defeats player j , tij = 0 if player i loses to player j , and tii = 0. Thus T has 0's along the main diagonal, and in the off-diagonal positions T satisfies the "skew-symmetry" condition that tij = 1 if and only if tji = 0. We call such a (0, 1)-matrix T a tournament matrix.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 957 - 969
Copyright
Copyright © Canadian Mathematical Society 1965

References

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4. Ryser, H. J., Matrices of zeros and ones in combinatorial mathematics, Recent Advances in Matrix Theory (Madison, Wis., 1964).Google Scholar