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- Dilworths_theorem abstract "In mathematics, in the areas of order theory and combinatorics, Dilworth's theorem characterizes the width of any finite partially ordered set in terms of a partition of the order into a minimum number of chains. It is named for the mathematician Robert P. Dilworth (1950).An antichain in a partially ordered set is a set of elements no two of which are comparable to each other, and a chain is a set of elements every two of which are comparable. Dilworth's theorem states that there exists an antichain A, and a partition of the order into a family P of chains, such that the number of chains in the partition equals the cardinality of A. When this occurs, A must be the largest antichain in the order, for any antichain can have at most one element from each member of P. Similarly, P must be the smallest family of chains into which the order can be partitioned, for any partition into chains must have at least one chain per element of A. The width of the partial order is defined as the common size of A and P.An equivalent way of stating Dilworth's theorem is that, in any finite partially ordered set, the maximum number of elements in any antichain equals the minimum number of chains in any partition of the set into chains. A version of the theorem for infinite partially ordered sets states that, in this case, a partially ordered set has finite width w if and only if it may be partitioned into w chains, but not less.".
- Dilworths_theorem thumbnail Dilworth-via-König.svg?width=300.
- Dilworths_theorem wikiPageExternalLink DualOfDilworthsTheorem.html.
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- Dilworths_theorem wikiPageExternalLink 10.pdf.
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- Dilworths_theorem wikiPageWikiLink Abouabdillahs_theorem.
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- Dilworths_theorem wikiPageWikiLink Annals_of_Mathematics.
- Dilworths_theorem wikiPageWikiLink Antichain.
- Dilworths_theorem wikiPageWikiLink Antimatroid.
- Dilworths_theorem wikiPageWikiLink Bipartite_graph.
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- Dilworths_theorem wikiPageWikiLink Category:Articles_containing_proofs.
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- Dilworths_theorem wikiPageWikiLink Category:Theorems_in_combinatorics.
- Dilworths_theorem wikiPageWikiLink Clique_(graph_theory).
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- Dilworths_theorem wikiPageWikiLink Complement_graph.
- Dilworths_theorem wikiPageWikiLink De_Bruijn–Erdős_theorem_(graph_theory).
- Dilworths_theorem wikiPageWikiLink Discrete_Mathematics_(journal).
- Dilworths_theorem wikiPageWikiLink Divisibility_rule.
- Dilworths_theorem wikiPageWikiLink Erdős–Szekeres_theorem.
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- Dilworths_theorem wikiPageWikiLink Halls_marriage_theorem.
- Dilworths_theorem wikiPageWikiLink Independent_set_(graph_theory).
- Dilworths_theorem wikiPageWikiLink Induced_subgraph.
- Dilworths_theorem wikiPageWikiLink Kxc5x91nigs_theorem_(graph_theory).
- Dilworths_theorem wikiPageWikiLink Lubell–Yamamoto–Meshalkin_inequality.
- Dilworths_theorem wikiPageWikiLink Mathematics.
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- Dilworths_theorem wikiPageWikiLink Order_dimension.
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- Dilworths_theorem wikiPageWikiLink Partially_ordered_set.
- Dilworths_theorem wikiPageWikiLink Partition_of_a_set.
- Dilworths_theorem wikiPageWikiLink Perfect_graph.
- Dilworths_theorem wikiPageWikiLink Perfect_graph_theorem.
- Dilworths_theorem wikiPageWikiLink PlanetMath.
- Dilworths_theorem wikiPageWikiLink Power_set.
- Dilworths_theorem wikiPageWikiLink Proceedings_of_the_American_Mathematical_Society.
- Dilworths_theorem wikiPageWikiLink Sperners_theorem.
- Dilworths_theorem wikiPageWikiLink Subset.
- Dilworths_theorem wikiPageWikiLink Time_complexity.
- Dilworths_theorem wikiPageWikiLink File:Dilworth-via-König.svg.
- Dilworths_theorem wikiPageWikiLinkText "Dilworth's theorem".
- Dilworths_theorem wikiPageWikiLinkText "width".
- Dilworths_theorem authorlink "Robert P. Dilworth".
- Dilworths_theorem first "Robert P.".
- Dilworths_theorem last "Dilworth".
- Dilworths_theorem title "Dilworth's Lemma".
- Dilworths_theorem urlname "DilworthsLemma".
- Dilworths_theorem wikiPageUsesTemplate Template:Citation.
- Dilworths_theorem wikiPageUsesTemplate Template:Harv.
- Dilworths_theorem wikiPageUsesTemplate Template:Harvs.
- Dilworths_theorem wikiPageUsesTemplate Template:Harvtxt.
- Dilworths_theorem wikiPageUsesTemplate Template:Main.
- Dilworths_theorem wikiPageUsesTemplate Template:Mathworld.
- Dilworths_theorem year "1950".
- Dilworths_theorem subject Category:Articles_containing_proofs.
- Dilworths_theorem subject Category:Order_theory.
- Dilworths_theorem subject Category:Perfect_graphs.
- Dilworths_theorem subject Category:Theorems_in_combinatorics.
- Dilworths_theorem type Combinatoric.
- Dilworths_theorem type Field.
- Dilworths_theorem type Graph.
- Dilworths_theorem type Proof.
- Dilworths_theorem type Theorem.
- Dilworths_theorem comment "In mathematics, in the areas of order theory and combinatorics, Dilworth's theorem characterizes the width of any finite partially ordered set in terms of a partition of the order into a minimum number of chains. It is named for the mathematician Robert P. Dilworth (1950).An antichain in a partially ordered set is a set of elements no two of which are comparable to each other, and a chain is a set of elements every two of which are comparable.".
- Dilworths_theorem label "Dilworth's theorem".
- Dilworths_theorem sameAs Q1134776.
- Dilworths_theorem sameAs Satz_von_Dilworth.
- Dilworths_theorem sameAs نظریه_دیلورث.
- Dilworths_theorem sameAs Théorème_de_Dilworth.
- Dilworths_theorem sameAs 딜워스의_정리.
- Dilworths_theorem sameAs m.038280.
- Dilworths_theorem sameAs Теорема_Дилуорса.
- Dilworths_theorem sameAs Теорема_Ділуорса.
- Dilworths_theorem sameAs Q1134776.
- Dilworths_theorem wasDerivedFrom Dilworths_theorem?oldid=702998328.
- Dilworths_theorem depiction Dilworth-via-König.svg.
- Dilworths_theorem isPrimaryTopicOf Dilworths_theorem.