I need a formula for maximum number of hyperedges that a directed hypergraph with *n* vertices can have. Following point is an unresolved issues for me and it keeps coming back to my mind:

- There are different definitions for hyperedges in directed hypergraphs (e.g. some say a hyperedge e = (T(e), H(e)) in which T(e) and H(e) cannot be empty set, some say they H(e) can be empty set). Is there a standart definition I'm missing?