Nonconvexity of the Set of Hypergraph Degree Sequences

It is well known that the set of possible degree sequences for a simple graph on n vertices is the intersection of a lattice and a convex polytope. We show that the set of possible degree sequences for a simple k-uniform hypergraph on n vertices is not the intersection of a lattice and a convex polytope for k > 3 and n > k + 13. We also show an analogous nonconvexity result for the set of degree sequences of kpartite k-uniform hypergraphs and the generalized notion of λ-balanced k-uniform hypergraphs.