On Scores, Losing Scores And Total Scores In K-Hypertournaments

A k-hypertournament is a complete k-hypergraph with each k-edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a k-hypertournament, the score s(i) (losing score r(i)) of a vertex v(i) is the number of arcs containing v(i) in which v(i) is not the last element (in which v(i) is the last element). The total score of v(i) is defined as t(i) = s(i) - r(i). In this paper we obtain stronger inequalities for the quantities Sigma(i is an element of I)r(i), Sigma(i is an element of I) s(i) and Sigma(i is an element of I) t(i), where I subset of {1, 2, ..., n}. Furthermore, we discuss the case of equality for these inequalities. We also characterize total score sequences of strong k-hypertournaments.