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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 thatthe 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 $k \geq3$ and $n \geq k+13$. We also show an analogous nonconvexity result for the setof degree sequences of $k$-partite $k$-uniform hypergraphs and the generalizednotion of $\lambda$-balanced $k$-uniform hypergraphs.

Nonconvexity of the set of hypergraph degree sequences