The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 8 Issue 2
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- Pages.185-191
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- 2001
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
SCORE SEQUENCES OF HYPERTOURNAMENT MATRICES
- Koh, Young-Mee (Department of Mathematics, University of Suwon) ;
- Ree, Sang-Wook (Department of Mathematics, University of Suwon)
- Published : 2001.11.01
Abstract
A k-hypertournament is a complete k-hypergraph with all k-edges endowed with orientations, i.e., orderings of the vertices in the edges. The incidence matrix associated with a k-hypertournament is called a 7-hypertournament matrix, where each row stands for a vertex of the hypertournament. Some properties of the hypertournament matrices are investigated. The sequences of the numbers of 1's and -1's of rows of a k-hypertournament matrix are respectively called the score sequence (resp. losing score sequence) of the matrix and so of the corresponding hypertournament. A necessary and sufficient condition for a sequence to be the score sequence (resp. the losing score sequence) of a k-hypertournament is proved.