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This article seems kind of schizophrenic, with the
Dedekind number and Clutter sections only being about Sperner families (and not Sperner's theorem) while the Proof and Generalizations sections are only about Sperner's theorem (and not about Sperner families). Maybe it would benefit from being split
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I changed the field from "foundations" (Foundations and set theory) to "discrete" (Discrete math), because
Sperner theory is part of combinatorics, not part of foundations of math or its relative, abstract set theory. It happens to be about sets, but not about properties of sets themselves. It
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Example 1 claims that the blockers of a graph are the minimal dominating sets, but this is easily seen to be false: consider the 4-vertex path a-b-c-d. Then {a,d} is dominating (and minimal), yet not a blocker as it doesn't intersect the edge b-c. Perhaps the author meant that the blockers are
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Uhhhmmm, seems like maybe not ... it seems we should merge that article into this one. An alternative would be to rename this article to be "Sperner's theorem", mention this theorem from the clutter article, and redirect "Sperner system" to point at "clutter".
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Is it necessary (or even appropriate) to over-divide such a short article into tiny sections? Also, the Q.E.D. thing is cute, but the hollow square notation is more consistent with mainstream mathematical
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belongs to the subfield of combinatorics, often called "extremal set theory" or "combinatorics of finite sets", that concerns relations between (finite) sets.
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Also, this article should say what E is. I assume X and Y are subsets of E, but the definition should say that.
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for that content in the latter page, and it must not be deleted as long as the latter page exists.
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Knowledge. If you would like to participate, please visit the project page, where you can join
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Done, although the clutter material is not as polished as what was already here.
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I think "Sperner family" is more commonly used than "clutter", and so
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It is also called an antichain in combinatorics, though the article
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There are many short topics. Each could be expanded (
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Is there a difference between a
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