SCORE SEQUENCES OF HYPERTOURNAMENT MATRICES

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.