It is well known that the set of possible degree sequences for a 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 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 k-partite k-uniform hypergraphs and the generalized
notion of λ-balanced k-uniform hypergraphs.Comment: 5 page