Degree sequences of sufficiently dense random uniform hypergraphs

Abstract We find an asymptotic enumeration formula for the number of simple $r$ -uniform hypergraphs with a given degree sequence, when edges is sufficiently large. The in terms solution system equations. give sufficient conditions on sequence which guarantee existence to this system. Furthermore, we solve and explicit close regular. This allows us establish several properties random hypergraph edges. More specifically, compare certain models involving sequences binomial or hypergeometric variables conditioned their sum.