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Hypergraphs are structures that can be decomposed or described; in otherwords they are recursively countable. Here, we get exact and asymptoticenumeration results on hypergraphs by means of exponential generatingfunctions. The number of hypergraph component is bounded, as a generalisationof Wright inequalities for graphs: the proof is a combinatorial understandingof the structure by inclusion exclusion. Asymptotic results are obtained,thanks to generating functions proofs are at the end very easy to read, throughcomplex analysis by saddle point method. By this way, we characterized:  - the components with a given number of vertices and of hyperedges by theexpected size of a random hypermatching in these structures.  - the random hypergraphs (evolving hyperedge by hyperedge) according to theexpected number of hyperedges when the first cycle appears in the evolvingstructure.  This work is an open road to further works on random hypergraphs such asthreshold phenomenon, tools used here seem to be sufficient at first sight.

Random hypergraphs and algorithmics