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- Dilworth's_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.".
- Dilworth's_theorem thumbnail Dilworth-via-König.svg?width=300.
- Dilworth's_theorem wikiPageExternalLink books?id=FYV6tGm3NzgC&pg=PA59.
- Dilworth's_theorem wikiPageExternalLink DualOfDilworthsTheorem.html.
- Dilworth's_theorem wikiPageExternalLink GS-05R-1.pdf.
- Dilworth's_theorem wikiPageExternalLink VOTMSTOEAS.pdf.
- Dilworth's_theorem wikiPageExternalLink 10.pdf.
- Dilworth's_theorem wikiPageID "749033".
- Dilworth's_theorem wikiPageRevisionID "606205166".
- Dilworth's_theorem authorlink "Robert P. Dilworth".
- Dilworth's_theorem first "Robert P.".
- Dilworth's_theorem hasPhotoCollection Dilworth's_theorem.
- Dilworth's_theorem last "Dilworth".
- Dilworth's_theorem title "Dilworth's Lemma".
- Dilworth's_theorem urlname "DilworthsLemma".
- Dilworth's_theorem year "1950".
- Dilworth's_theorem subject Category:Articles_containing_proofs.
- Dilworth's_theorem subject Category:Order_theory.
- Dilworth's_theorem subject Category:Perfect_graphs.
- Dilworth's_theorem subject Category:Theorems_in_combinatorics.
- Dilworth's_theorem type Abstraction100002137.
- Dilworth's_theorem type Communication100033020.
- Dilworth's_theorem type Graph107000195.
- Dilworth's_theorem type Message106598915.
- Dilworth's_theorem type PerfectGraphs.
- Dilworth's_theorem type Proposition106750804.
- Dilworth's_theorem type Statement106722453.
- Dilworth's_theorem type Theorem106752293.
- Dilworth's_theorem type TheoremsInCombinatorics.
- Dilworth's_theorem type TheoremsInDiscreteMathematics.
- Dilworth's_theorem type VisualCommunication106873252.
- Dilworth's_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.".
- Dilworth's_theorem label "Dilworth's theorem".
- Dilworth's_theorem label "Satz von Dilworth".
- Dilworth's_theorem label "Théorème de Dilworth".
- Dilworth's_theorem label "Теорема Дилуорса".
- Dilworth's_theorem sameAs Satz_von_Dilworth.
- Dilworth's_theorem sameAs Théorème_de_Dilworth.
- Dilworth's_theorem sameAs 딜워스의_정리.
- Dilworth's_theorem sameAs m.038280.
- Dilworth's_theorem sameAs Q1134776.
- Dilworth's_theorem sameAs Q1134776.
- Dilworth's_theorem sameAs Dilworth's_theorem.
- Dilworth's_theorem wasDerivedFrom Dilworth's_theorem?oldid=606205166.
- Dilworth's_theorem depiction Dilworth-via-König.svg.
- Dilworth's_theorem isPrimaryTopicOf Dilworth's_theorem.
