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An antichain is here regarded as a hypergraph that satisfies the following property: neither of every two different edges is a subset of the other one. The paper is devoted to the enumeration of antichains given on an n-set and having one or more of the following properties: being labeled or unlabeled; being ordered or unordered; being a cover (or a proper cover); and finally, being a T 0 -, T 1 -or T 2 -hypergraph. The problem of enumeration of these classes comprises, in fact, differentdoi:10.2298/pim140406001k fatcat:c2qckfz4l5espa74t4bmmmjxaa