Score lists in [h-k]-bipartite hypertournaments

Abstract

Given non-negative integers m, n, h and k with $m\ge h>1$ and $n\ge k>1,$an [h-k]-bipartite hypertournament on $m+n$ vertices is a triple $(U,V,A)$, where U and V are two sets of vertices with $|U|=m$ and $|V|=n,$ and $A$ is a set of $(h+k)-$ tuples of vertices, called arcs, with exactly $h$ vertices from $U$ and exactly $k$ vertices from $V$, such that any $h+k$ subsets $U_1\cup V_1$ of $U\cup V,A$ contains exactly one of the $(h+k)!(h+k)-$tuples whose entries belong to $U_1\cup V_1.$ We obtain necessary and sufficient conditions for a pair of non-decreasing sequences of non-negative integers to be the losing score lists or score lists of some$[h-k]-$bipartite hypertournament.\bigskip