Score Lists in Tripartite Hypertournaments

Given non-negative integers l, m, n, α, β and γ with l ≥ α ≥ 1, m ≥ β ≥ 1 and n ≥ γ ≥ 1, an α,β,γ]-tripartite hypertournament on l + m + n vertices is a four tuple (U, V, W, E), where U, V and W are three sets of vertices with |U| = l , |V| = m and |W| = n, and E is a set of (α + β + γ)-tuples of vertices, called arcs, with exactly α vertices from U, exactly β vertices from V,and exactly γ vertices from W, such that any subset U₁∪ V₁∪ W₁ of U∪ V∪ W, E contains exactly one of the (α + β + γ)! (α + β + γ) − tuples whose entries belong to U₁∪ V₁∪ W₁. We obtain necessary and sufficient conditions for three lists of non-negative integers in non-decreasing order to be the losing score lists or score lists of some α, β, γ]-tripartite hypertournament. Supported by National Science Foundation of China (No.10501021).