Asymptotic enumeration formulas for dihypergraphs with given in/out-degree sequences and specified head/tail sizes, valid under bounded maxima.
Qian, Enumeration of unlabelled directed hypergraphs, Electronic Journal of Com- binatorics 20(1) (2013), #P.46
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Enumeration of dihypergraphs with specified degrees and edge types
Asymptotic enumeration formulas for dihypergraphs with given in/out-degree sequences and specified head/tail sizes, valid under bounded maxima.