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In combinatorics, a Sperner family (or Sperner system), named in honor of Emanuel Sperner, is a family of sets (''F'', ''E'') in which none of the sets is contained in another. Equivalently, a Sperner family is an antichain in the inclusion lattice over the power set of ''E''. A Sperner family is also sometimes called an independent system or a clutter. Sperner families are counted by the Dedekind numbers, and their size is bounded by Sperner's theorem and the Lubell–Yamamoto–Meshalkin inequality. They may also be described in the language of hypergraphs rather than set families, where they are called clutters. ==Dedekind numbers== (詳細はDedekind numbers, the first few of which are :2, 3, 6, 20, 168, 7581, 7828354, 2414682040998, 56130437228687557907788 . Although accurate asymptotic estimates are known for larger values of ''n'', it is unknown whether there exists an exact formula that can be used to compute these numbers efficiently. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sperner family」の詳細全文を読む スポンサード リンク
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