Note on the degree sequences of kk-hypertournaments

We obtain a criterion for determining whether or not a non-decreasing sequence of non-negative integers is a degree sequence of some kk-hypertournament on nn vertices. This result generalizes the corresponding theorems on tournaments proposed by Landau [H.G. Landau, On dominance relations and the structure of animal societies. III. The condition for a score structure, Bull. Math. Biophys. 15 (1953) 143–148] in 1953.