On score sequences of \(k\)-hypertournaments
For a pair \((n,k)\) of natural numbers with \(n\geq k>1\), a \(k\)-hypertournament on \(n\) vertices is a pair \((V,A)\), where \(V\) is a set of vertices, \(|V|= n\), and \(A\) is a set of \(k\)-tuples of vertices, called arcs, such that for any \(k\)-subset \(S\) of \(V\), \(A\) contains exactly one of the \(k!\) \(k\)-tuples whose elements belong to \(S\). In particular, a 2-hypertournament is an (ordinary) tournament. The authors characterise score sequences of \(k\)-hypertournaments and, thus, generalise Landau's result for tournaments.
scientific article; zbMATH DE number 1545622