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- Sperners_lemma abstract "You may be looking for Sperner's theorem on set familiesIn mathematics, Sperner's lemma is a combinatorial analog of the Brouwer fixed point theorem, which is equivalent to it. Sperner's lemma states that every Sperner coloring (described below) of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain. Sperner colorings have been used for effective computation of fixed points and in root-finding algorithms, and are applied in fair division (cake cutting) algorithms. It is now believed to be an intractable computational problem to find a Brouwer fixed point or equivalently a Sperner coloring even in the plane, in the general case. The problem is PPAD-complete, a complexity class invented by Christos Papadimitriou.According to the Soviet Mathematical Encyclopaedia (ed. I.M. Vinogradov), a related 1929 theorem (of Knaster, Borsuk and Mazurkiewicz) has also become known as the Sperner lemma – this point is discussed in the English translation (ed. M. Hazewinkel). It is now commonly known as the Knaster–Kuratowski–Mazurkiewicz lemma.".
- Sperners_lemma thumbnail Sperner1d.svg?width=300.
- Sperners_lemma wikiPageExternalLink SpernerLemma.shtml.
- Sperners_lemma wikiPageID "465067".
- Sperners_lemma wikiPageLength "9633".
- Sperners_lemma wikiPageOutDegree "43".
- Sperners_lemma wikiPageRevisionID "664158253".
- Sperners_lemma wikiPageWikiLink Analogy.
- Sperners_lemma wikiPageWikiLink Bronisław_Knaster.
- Sperners_lemma wikiPageWikiLink Brouwer_fixed-point_theorem.
- Sperners_lemma wikiPageWikiLink Category:Articles_containing_proofs.
- Sperners_lemma wikiPageWikiLink Category:Combinatorics.
- Sperners_lemma wikiPageWikiLink Category:Fair_division.
- Sperners_lemma wikiPageWikiLink Category:Fixed_points_(mathematics).
- Sperners_lemma wikiPageWikiLink Category:Lemmas.
- Sperners_lemma wikiPageWikiLink Category:Topology.
- Sperners_lemma wikiPageWikiLink Christos_Papadimitriou.
- Sperners_lemma wikiPageWikiLink Combinatorics.
- Sperners_lemma wikiPageWikiLink Cut-the-Knot.
- Sperners_lemma wikiPageWikiLink Emanuel_Sperner.
- Sperners_lemma wikiPageWikiLink Equidissection.
- Sperners_lemma wikiPageWikiLink Fair_division.
- Sperners_lemma wikiPageWikiLink Fixed_point_(mathematics).
- Sperners_lemma wikiPageWikiLink Function_(mathematics).
- Sperners_lemma wikiPageWikiLink Handshaking_lemma.
- Sperners_lemma wikiPageWikiLink Intermediate_value_theorem.
- Sperners_lemma wikiPageWikiLink Invariance_of_domain.
- Sperners_lemma wikiPageWikiLink Ivan_Matveyevich_Vinogradov.
- Sperners_lemma wikiPageWikiLink Karol_Borsuk.
- Sperners_lemma wikiPageWikiLink Knaster–Kuratowski–Mazurkiewicz_lemma.
- Sperners_lemma wikiPageWikiLink Krassimir_Atanassov.
- Sperners_lemma wikiPageWikiLink Mathematics.
- Sperners_lemma wikiPageWikiLink Monskys_theorem.
- Sperners_lemma wikiPageWikiLink PPAD_(complexity).
- Sperners_lemma wikiPageWikiLink Polytope.
- Sperners_lemma wikiPageWikiLink Root-finding_algorithm.
- Sperners_lemma wikiPageWikiLink Simmons–Su_protocols.
- Sperners_lemma wikiPageWikiLink Simplex.
- Sperners_lemma wikiPageWikiLink Sperners_theorem.
- Sperners_lemma wikiPageWikiLink Stefan_Mazurkiewicz.
- Sperners_lemma wikiPageWikiLink Topological_combinatorics.
- Sperners_lemma wikiPageWikiLink Triangle.
- Sperners_lemma wikiPageWikiLink Triangulation_(geometry).
- Sperners_lemma wikiPageWikiLink File:Sperner1d.svg.
- Sperners_lemma wikiPageWikiLink File:Sperner2d.svg.
- Sperners_lemma wikiPageWikiLink File:Spernergraph.svg.
- Sperners_lemma wikiPageWikiLink File:Spernerlemma.svg.
- Sperners_lemma wikiPageWikiLinkText "Sperner's lemma coloring".
- Sperners_lemma wikiPageWikiLinkText "Sperner's lemma".
- Sperners_lemma wikiPageWikiLinkText "generalization of Sperner's lemma to polytopes".
- Sperners_lemma wikiPageUsesTemplate Template:Analogous_fixed-point_theorems.
- Sperners_lemma subject Category:Articles_containing_proofs.
- Sperners_lemma subject Category:Combinatorics.
- Sperners_lemma subject Category:Fair_division.
- Sperners_lemma subject Category:Fixed_points_(mathematics).
- Sperners_lemma subject Category:Lemmas.
- Sperners_lemma subject Category:Topology.
- Sperners_lemma hypernym Analog.
- Sperners_lemma type Drug.
- Sperners_lemma type Combinatoric.
- Sperners_lemma type Field.
- Sperners_lemma type Lemma.
- Sperners_lemma type Proof.
- Sperners_lemma type Redirect.
- Sperners_lemma type Theorem.
- Sperners_lemma comment "You may be looking for Sperner's theorem on set familiesIn mathematics, Sperner's lemma is a combinatorial analog of the Brouwer fixed point theorem, which is equivalent to it. Sperner's lemma states that every Sperner coloring (described below) of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain.".
- Sperners_lemma label "Sperner's lemma".
- Sperners_lemma sameAs Q733336.
- Sperners_lemma sameAs Lemma_von_Sperner.
- Sperners_lemma sameAs Lemme_de_Sperner.
- Sperners_lemma sameAs הלמה_של_שפרנר.
- Sperners_lemma sameAs Sperner-lemma.
- Sperners_lemma sameAs Lemma_di_Sperner.
- Sperners_lemma sameAs m.02cs15.
- Sperners_lemma sameAs Лемма_Шпернера.
- Sperners_lemma sameAs Q733336.
- Sperners_lemma wasDerivedFrom Sperners_lemma?oldid=664158253.
- Sperners_lemma depiction Sperner1d.svg.
- Sperners_lemma isPrimaryTopicOf Sperners_lemma.