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- Topological_combinatorics abstract "The discipline of combinatorial topology used combinatorial concepts in topology and in the early 20th century this turned into the field of algebraic topology.In 1978 the situation was reversed – methods from algebraic topology were used to solve a problem in combinatorics – when László Lovász proved the Kneser conjecture, thus beginning the new study of topological combinatorics. Lovász's proof used the Borsuk-Ulam theorem and this theorem retains a prominent role in this new field. This theorem has many equivalent versions and analogs and has been used in the study of fair division problems.In another application of homological methods to graph theory Lovász proved both the undirected and directed versions of a conjecture of Frank: Given a k-connected graph G, k points v1,...,vk∈ V(G), and k positive integers n1,n2,...,nk that sum up to |V(G)|, there exists a partition {V1,...,Vk} of V(G) such that vi∈ Vi, |Vi|=ni and Vi spans a connected subgraph.In 1987 the necklace splitting problem was solved by Noga Alon using the Borsuk-Ulam theorem. It has also been used to study complexity problems in linear decision tree algorithms and the Aanderaa–Karp–Rosenberg conjecture. Other areas include topology of partially ordered sets and bruhat orders.Additionally, methods from differential topology now have a combinatorial analog in discrete Morse theory.".
- Topological_combinatorics wikiPageExternalLink lange_carsten.pdf.
- Topological_combinatorics wikiPageExternalLink TopMeth.pdf.
- Topological_combinatorics wikiPageID "17633579".
- Topological_combinatorics wikiPageLength "4370".
- Topological_combinatorics wikiPageOutDegree "29".
- Topological_combinatorics wikiPageRevisionID "636283196".
- Topological_combinatorics wikiPageWikiLink Aanderaa–Karp–Rosenberg_conjecture.
- Topological_combinatorics wikiPageWikiLink Algebraic_topology.
- Topological_combinatorics wikiPageWikiLink András_Frank.
- Topological_combinatorics wikiPageWikiLink Borsuk–Ulam_theorem.
- Topological_combinatorics wikiPageWikiLink Bruhat_order.
- Topological_combinatorics wikiPageWikiLink Category:Algebraic_topology.
- Topological_combinatorics wikiPageWikiLink Category:Combinatorics.
- Topological_combinatorics wikiPageWikiLink Category:Topology.
- Topological_combinatorics wikiPageWikiLink Combinatorial_topology.
- Topological_combinatorics wikiPageWikiLink Combinatorics.
- Topological_combinatorics wikiPageWikiLink Computational_complexity_theory.
- Topological_combinatorics wikiPageWikiLink Decision_tree.
- Topological_combinatorics wikiPageWikiLink Differential_topology.
- Topological_combinatorics wikiPageWikiLink Discrete_Morse_theory.
- Topological_combinatorics wikiPageWikiLink Discrete_exterior_calculus.
- Topological_combinatorics wikiPageWikiLink Fair_division.
- Topological_combinatorics wikiPageWikiLink Finite_topological_space.
- Topological_combinatorics wikiPageWikiLink Graph_theory.
- Topological_combinatorics wikiPageWikiLink Homology_(mathematics).
- Topological_combinatorics wikiPageWikiLink Kneser_graph.
- Topological_combinatorics wikiPageWikiLink László_Lovász.
- Topological_combinatorics wikiPageWikiLink Necklace_splitting_problem.
- Topological_combinatorics wikiPageWikiLink Noga_Alon.
- Topological_combinatorics wikiPageWikiLink Poset_topology.
- Topological_combinatorics wikiPageWikiLink Sperners_lemma.
- Topological_combinatorics wikiPageWikiLink Technical_University_of_Berlin.
- Topological_combinatorics wikiPageWikiLink Topological_graph_theory.
- Topological_combinatorics wikiPageWikiLink Topology.
- Topological_combinatorics wikiPageWikiLinkText "Topological combinatorics".
- Topological_combinatorics wikiPageWikiLinkText "topological combinatorics".
- Topological_combinatorics wikiPageWikiLinkText "topological".
- Topological_combinatorics wikiPageUsesTemplate Template:Citation.
- Topological_combinatorics subject Category:Algebraic_topology.
- Topological_combinatorics subject Category:Combinatorics.
- Topological_combinatorics subject Category:Topology.
- Topological_combinatorics hypernym Methods.
- Topological_combinatorics type Software.
- Topological_combinatorics type Combinatoric.
- Topological_combinatorics type Field.
- Topological_combinatorics comment "The discipline of combinatorial topology used combinatorial concepts in topology and in the early 20th century this turned into the field of algebraic topology.In 1978 the situation was reversed – methods from algebraic topology were used to solve a problem in combinatorics – when László Lovász proved the Kneser conjecture, thus beginning the new study of topological combinatorics. Lovász's proof used the Borsuk-Ulam theorem and this theorem retains a prominent role in this new field.".
- Topological_combinatorics label "Topological combinatorics".
- Topological_combinatorics sameAs Q256108.
- Topological_combinatorics sameAs توافقيات_طوبولوجية.
- Topological_combinatorics sameAs Topologische_Kombinatorik.
- Topological_combinatorics sameAs m.0463l9z.
- Topological_combinatorics sameAs Q256108.
- Topological_combinatorics wasDerivedFrom Topological_combinatorics?oldid=636283196.
- Topological_combinatorics isPrimaryTopicOf Topological_combinatorics.