Families of sets

Sperner family

In combinatorics, a Sperner family (or Sperner system; named in honor of Emanuel Sperner), or clutter, is a family F of subsets of a finite set E in which none of the sets contains 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 irredundant set. 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. (Wikipedia).

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Related pages

Abstract simplicial complex | Menger's theorem | Vertex cover | Sperner's theorem | The Art of Computer Programming | Bipartite graph | Dedekind number | Journal of Combinatorial Theory | Combinatorics | Asymptotic expansion | Family of sets | Antichain | Kőnig's theorem (graph theory) | Lubell–Yamamoto–Meshalkin inequality | Hypergraph | Power set | Lattice (order)