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, thescore si (losing score ri) of a vertex vi is the number of arcs containing vi in which vi is not thelast element (in which vi is the last element). The total score of vi is defined as ti = si - ri. Inthis paper we obtain stronger inequalities for the quantities ∑iЄI ri,∑iЄI si and ∑iЄI ti, where I (subseteq){1; 2; : : : ; n}. Furthermore, we discuss the case of equality for these inequalities. We also characterize total score sequences of strong k-hypertournaments.