Multipartite entanglement in qudit hypergraph states

We study entanglement properties of hypergraph states in arbitrary finite dimension. compute multipartite elementary qudit states, namely those endowed with a single maximum-cardinality hyperedge. show that, analogously to the qubit case, also for dimension there exists lower bound connected states; this is given by an equal-dimension state featuring same number qudits as largest-cardinality highlight interesting differences between prime and non-prime features.