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On Scores, Losing Scores and Total Scores in Hypertournaments
A -hypertournament is a complete -hypergraph with each -edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a -hypertournament, the score (losing score ) of a vertex is the number of arcs containing in which is not the last element (in which is the last element). The total score of is defined as . In this paper we obtain stronger inequalities for the quantities , and , where . Furthermore, we discuss the case of equality for these inequalities. We also characterize total score sequences of strong -hypertournaments