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- Antichain abstract "In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable. (Some authors use the term \"antichain\" to mean strong antichain, a subset such that there is no element of the poset smaller than two distinct elements of the antichain.)Let S be a partially ordered set. We say two elements a and b of a partially ordered set are comparable if a ≤ b or b ≤ a. If two elements are not comparable, we say they are incomparable; that is, x and y are incomparable if neither x ≤ y nor y ≤ x.A chain in S is a subset C of S in which each pair of elements is comparable; that is, C is totally ordered. An antichain in S is a subset A of S in which each pair of different elements is incomparable; that is, there is no order relation between any two different elements in A.".
- Antichain wikiPageID "348973".
- Antichain wikiPageLength "4237".
- Antichain wikiPageOutDegree "23".
- Antichain wikiPageRevisionID "701509085".
- Antichain wikiPageWikiLink Ascending_chain_condition.
- Antichain wikiPageWikiLink Birkhoffs_representation_theorem.
- Antichain wikiPageWikiLink Category:Integer_sequences.
- Antichain wikiPageWikiLink Category:Order_theory.
- Antichain wikiPageWikiLink Comparability.
- Antichain wikiPageWikiLink Dedekind_number.
- Antichain wikiPageWikiLink Dilworths_theorem.
- Antichain wikiPageWikiLink Distributive_lattice.
- Antichain wikiPageWikiLink Mathematics.
- Antichain wikiPageWikiLink Mirskys_theorem.
- Antichain wikiPageWikiLink Order_theory.
- Antichain wikiPageWikiLink Partially_ordered_set.
- Antichain wikiPageWikiLink Sperner_family.
- Antichain wikiPageWikiLink Strong_antichain.
- Antichain wikiPageWikiLink Subset.
- Antichain wikiPageWikiLink Total_order.
- Antichain wikiPageWikiLink Upper_set.
- Antichain wikiPageWikiLinkText "Antichain".
- Antichain wikiPageWikiLinkText "Antichain#Height_and_width".
- Antichain wikiPageWikiLinkText "antichain".
- Antichain wikiPageWikiLinkText "antichains".
- Antichain wikiPageWikiLinkText "chain".
- Antichain wikiPageWikiLinkText "height".
- Antichain wikiPageWikiLinkText "number of antichains".
- Antichain wikiPageWikiLinkText "width".
- Antichain id "3212".
- Antichain title "Antichain".
- Antichain urlname "Antichain".
- Antichain wikiPageUsesTemplate Template:Mathworld.
- Antichain wikiPageUsesTemplate Template:OEIS.
- Antichain wikiPageUsesTemplate Template:Planetmath_reference.
- Antichain subject Category:Integer_sequences.
- Antichain subject Category:Order_theory.
- Antichain hypernym Subset.
- Antichain type ProgrammingLanguage.
- Antichain type Combinatoric.
- Antichain type Field.
- Antichain type Integer.
- Antichain comment "In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two elements in the subset are incomparable. (Some authors use the term \"antichain\" to mean strong antichain, a subset such that there is no element of the poset smaller than two distinct elements of the antichain.)Let S be a partially ordered set. We say two elements a and b of a partially ordered set are comparable if a ≤ b or b ≤ a.".
- Antichain label "Antichain".
- Antichain sameAs Q431937.
- Antichain sameAs Protiřetězec.
- Antichain sameAs Antikette.
- Antichain sameAs Anticadena.
- Antichain sameAs Antiketju.
- Antichain sameAs Antichaîne.
- Antichain sameAs Anticadea.
- Antichain sameAs Antilánc.
- Antichain sameAs 반사슬.
- Antichain sameAs Antyłańcuch.
- Antichain sameAs m.01z0lp.
- Antichain sameAs Protireťazec.
- Antichain sameAs Антиланцюг.
- Antichain sameAs Q431937.
- Antichain sameAs 反链.
- Antichain wasDerivedFrom Antichain?oldid=701509085.
- Antichain isPrimaryTopicOf Antichain.