On k-hypertournament matrices

A k-hypertournament is a complete k-hypergraph with all k-edges endowed with orientations. The incidence matrix associated with a k-hypertournament is called a k-hypertournament matrix. 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 and the losing score sequence of the matrix and so of the corresponding hypertournament. A necessary and sufficient condition for a sequence to be the score (and losing score) sequence of a k-hypertournament is considered. We also find some conditions for the existence of k-hypertournament matrices with constant score sequence, called regular k-hypertournament matrices.