On scores, losing scores and total scores in hypertournaments - Shariefuddin Pirzada; Muhammad Ali Khan; Zhou Guofei; Koko K Kayibi (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2015)
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 _iIr_i, _iIs_i and _iIt_i, where I{ 1,2,…,n}. Furthermore, we discuss the case of equality for these inequalities. We also characterize total score sequences of strong k-hypertournaments.