Talk:Sperner family

Text and/or other creative content from Clutter (mathematics) was copied or moved into Sperner family with this edit. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists.

Style[edit]

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 practices.
Peter Kwok 00:18, 2004 Jun 30 (UTC)

There's nothing wrong with Q.E.D. Zaslav (talk) 07:00, 8 November 2012 (UTC)[reply]

There are many short topics. Each could be expanded (invitation!), but they are distinct, so they should have sections, IMO. Zaslav (talk) 05:02, 24 January 2013 (UTC)[reply]

Clutter[edit]

Is there a difference between a Sperner family and a clutter? (See the other wiki page?) —Preceding unsigned comment added by 134.169.35.183 (talk) 09:31, 29 April 2008 (UTC)[reply]

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". linas (talk) 21:16, 4 May 2008 (UTC)[reply]

It is also called an antichain in combinatorics, though the article antichain is about the more general concept on posets —3mta3 (talk) 18:49, 27 May 2009 (UTC)[reply]

I think "Sperner family" is more commonly used than "clutter", and so clutter (mathematics) should be merged here.

Done, although the clutter material is not as polished as what was already here. xnn (talk) 23:30, 1 February 2010 (UTC)[reply]

Also, this article should say what E is. I assume X and Y are subsets of E, but the definition should say that. Rick Norwood (talk) 13:24, 11 August 2009 (UTC)[reply]

Incorrect Example?[edit]

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 exactly the minimal vertex covers (which is true)? Dotdotdotatsignapostrophe (talk) 14:45, 1 November 2011 (UTC)[reply]

Field of math[edit]

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 belongs to the subfield of combinatorics, often called "extremal set theory" or "combinatorics of finite sets", that concerns relations between (finite) sets. Zaslav (talk) 05:07, 24 January 2013 (UTC)[reply]

Split?[edit]

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 into two articles? —David Eppstein (talk) 05:58, 24 January 2013 (UTC)[reply]