@prefix foaf: <http://xmlns.com/foaf/0.1/> . <http://en.wikipedia.org/wiki/Erd\u0151s\u2013Szekeres_theorem> foaf:primaryTopic <http://dbpedia.org/resource/Erd\u0151s\u2013Szekeres_theorem> . @prefix dbo: <http://dbpedia.org/ontology/> . @prefix dbr: <http://dbpedia.org/resource/> . dbr:Convex_position dbo:wikiPageWikiLink <http://dbpedia.org/resource/Erd\u0151s\u2013Szekeres_theorem> . dbr:List_of_scientific_laws_named_after_people dbo:wikiPageWikiLink <http://dbpedia.org/resource/Erd\u0151s\u2013Szekeres_theorem> . @prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> . @prefix yago: <http://dbpedia.org/class/yago/> . <http://dbpedia.org/resource/Erd\u0151s\u2013Szekeres_theorem> rdf:type yago:Proposition106750804 , yago:Communication100033020 , yago:Cognition100023271 , yago:WikicatTheoremsInCombinatorics , yago:Form105930736 , yago:Structure105726345 , yago:Message106598915 , yago:Statement106722453 , yago:WikicatTheoremsInDiscreteMathematics , yago:WikicatTheoremsInDiscreteGeometry , yago:Abstraction100002137 , yago:WikicatPermutationPatterns , yago:Theorem106752293 , yago:PsychologicalFeature100023100 . @prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> . <http://dbpedia.org/resource/Erd\u0151s\u2013Szekeres_theorem> rdfs:label "Erd\u0151s\u2013Szekeres theorem"@en , "Th\u00E9or\u00E8me d'Erd\u0151s-Szekeres"@fr , "\u0645\u0628\u0631\u0647\u0646\u0629 \u0625\u064A\u0631\u062F\u0648\u0633-\u0633\u064A\u0643\u0631\u064A\u0633"@ar , "\u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u0415\u0440\u0434\u0435\u0448\u0430 \u2014 \u0421\u0435\u043A\u0435\u0440\u0435\u0448\u0430"@uk , "\uC5D0\uB974\uB418\uC2DC-\uC138\uCF00\uB808\uC2DC \uC815\uB9AC"@ko , "\u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u042D\u0440\u0434\u0451\u0448\u0430 \u2014 \u0421\u0435\u043A\u0435\u0440\u0435\u0448\u0430"@ru , "Teorema de Erd\u0151s-Szekeres"@es ; rdfs:comment "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u062A\u0646\u0635 \u0645\u0628\u0631\u0647\u0646\u0629 \u0625\u064A\u0631\u062F\u0648\u0633-\u0633\u064A\u0643\u0631\u064A\u0633 \u0639\u0644\u0649 \u0623\u0646\u0647 \u0641\u064A \u0643\u0644 \u0645\u062A\u062A\u0627\u0644\u064A\u0629 \u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u0623\u0639\u062F\u0627\u062F \u062D\u0642\u064A\u0642\u064A\u0629 \u0628\u0637\u0648\u0644 \u060C \u064A\u0648\u062C\u062F \u0644\u0647\u0627 \u0645\u062A\u062A\u0627\u0644\u064A\u0629 \u062C\u0632\u0626\u064A\u0629 \u0645\u062A\u0632\u0627\u064A\u062F\u0629 \u0628\u0637\u0648\u0644 \u0623\u0648 \u0645\u062A\u062A\u0627\u0644\u064A\u0629 \u062C\u0632\u0626\u064A\u0629 \u0645\u062A\u0646\u0627\u0642\u0635\u0629 \u0628\u0637\u0648\u0644 . \u0647\u0630\u0647 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0647\u064A \u0645\u0628\u0631\u0647\u0646\u0629 \u0645\u062B\u0627\u0644\u064A\u0629 \u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0631\u0645\u0632\u064A\u060C \u0627\u0644\u062A\u064A \u062A\u0628\u062D\u062B \u0627\u0644\u0627\u0646\u062A\u0638\u0627\u0645 \u0648\u0633\u0637 \u0627\u0644\u0641\u0648\u0636\u0649. \u062A\u0645\u062A \u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0639\u0644\u0649 \u064A\u062F \u0628\u0648\u0644 \u0625\u064A\u0631\u062F\u0648\u0633 \u0641\u064A \u0645\u0642\u0627\u0644 \u0644\u0647\u0645\u0627 \u0633\u0646\u0629 1935."@ar , "\uC218\uD559\uC5D0\uC11C \uC5D0\uB974\uB418\uC2DC-\uC138\uCF00\uB808\uC2DC \uC815\uB9AC\uB294 \uC8FC\uC5B4\uC9C4 , \uC5D0 \uB300\uD574 \uAE38\uC774\uAC00 \uC774\uC0C1\uC778 \uC11C\uB85C \uB2E4\uB978 \uC2E4\uC218\uB4E4\uC758 \uC218\uC5F4\uC740 \uAE38\uC774 \uC758 \uB2E8\uC870 \uC99D\uAC00\uD558\uB294 \uBD80\uBD84\uC218\uC5F4 \uB610\uB294 \uAE38\uC774 \uC758 \uB2E8\uC870 \uAC10\uC18C\uD558\uB294 \uBD80\uBD84\uC218\uC5F4\uC744 \uD3EC\uD568\uD55C\uB2E4\uB294 \uC815\uB9AC\uC774\uB2E4. \uC99D\uBA85\uC740 \uD574\uD53C \uC5D4\uB529 \uBB38\uC81C\uB97C \uC5B8\uAE09\uD55C \uB3D9\uC77C\uD55C 1935\uB144 \uB17C\uBB38\uC5D0 \uB098\uD0C0\uB0AC\uB2E4. \uC5D0\uB974\uB418\uC2DC-\uC138\uCF00\uB808\uC2DC \uC815\uB9AC\uB294 \uC815\uD655\uD788 \uB7A8\uC9C0\uC758 \uC815\uB9AC\uC758 \uB530\uB984\uC815\uB9AC\uAC00 \uB418\uB294 \uC720\uD55C\uD55C \uACB0\uACFC \uC911 \uD558\uB098\uC774\uB2E4. \uB7A8\uC9C0\uC758 \uC815\uB9AC\uB97C \uC0AC\uC6A9\uD558\uBA74 \uBAA8\uB4E0 \uC11C\uB85C \uB2E4\uB978 \uC2E4\uC218\uB85C \uC774\uB8E8\uC5B4\uC9C4 \uBB34\uD55C \uC218\uC5F4\uC774 \uB2E8\uC870 \uC99D\uAC00\uD558\uB294 \uBB34\uD55C \uBD80\uBD84 \uC218\uC5F4 \uB610\uB294 \uB2E8\uC870 \uAC10\uC18C\uD558\uB294 \uBB34\uD55C \uBD80\uBD84 \uC218\uC5F4\uC744 \uD3EC\uD568\uD55C\uB2E4\uB294 \uAC83\uC744 \uC27D\uAC8C \uC99D\uBA85\uD560 \uC218 \uC788\uC9C0\uB9CC \uC5D0\uB974\uB418\uC2DC \uD314\uACFC \uC138\uCF00\uB808\uC2DC \uC8C4\uB974\uC9C0\uAC00 \uC99D\uBA85\uD55C \uACB0\uACFC\uB294 \uB354 \uB098\uC544\uAC04\uB2E4."@ko , "In mathematics, the Erd\u0151s\u2013Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r \u2212 1)(s \u2212 1) + 1 contains a monotonically increasing subsequence of length r or a monotonically decreasing subsequence of length s. The proof appeared in the same 1935 paper that mentions the Happy Ending problem."@en , "\u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u042D\u0301\u0440\u0434\u0451\u0448\u0430 \u2014 \u0421\u0435\u0301\u043A\u0435\u0440\u0435\u0448\u0430 \u0432 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0435 \u2014 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043D\u0438\u0435, \u0443\u0442\u043E\u0447\u043D\u044F\u044E\u0449\u0435\u0435 \u043E\u0434\u043D\u043E \u0438\u0437 \u0441\u043B\u0435\u0434\u0441\u0442\u0432\u0438\u0439 \u0442\u0435\u043E\u0440\u0435\u043C\u044B \u0420\u0430\u043C\u0441\u0435\u044F \u0434\u043B\u044F \u0444\u0438\u043D\u0438\u0442\u043D\u043E\u0433\u043E \u0441\u043B\u0443\u0447\u0430\u044F. \u0412 \u0442\u043E \u0432\u0440\u0435\u043C\u044F \u043A\u0430\u043A \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0420\u0430\u043C\u0441\u0435\u044F \u043E\u0431\u043B\u0435\u0433\u0447\u0430\u0435\u0442 \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u043E \u0442\u043E\u0433\u043E, \u0447\u0442\u043E \u043A\u0430\u0436\u0434\u0430\u044F \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0440\u0430\u0437\u043D\u044B\u0445 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0441\u043E\u0434\u0435\u0440\u0436\u0438\u0442 \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0432\u043E\u0437\u0440\u0430\u0441\u0442\u0430\u044E\u0449\u0443\u044E \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u0443\u044E \u043F\u043E\u0434\u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0438\u043B\u0438 \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0443\u0431\u044B\u0432\u0430\u044E\u0449\u0443\u044E \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u0443\u044E \u043F\u043E\u0434\u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C, \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442, \u0434\u043E\u043A\u0430\u0437\u0430\u043D\u043D\u044B\u0439 \u041F\u0430\u043B\u043E\u043C \u042D\u0440\u0434\u0451\u0448\u0435\u043C \u0438 \u0414\u044C\u0451\u0440\u0434\u0435\u043C \u0421\u0435\u043A\u0435\u0440\u0435\u0448\u0435\u043C, \u0438\u0434\u0451\u0442 \u0434\u0430\u043B\u044C\u0448\u0435. \u0414\u043B\u044F \u0434\u0430\u043D\u043D\u044B\u0445 r, s \u043E\u043D\u0438 \u043F\u043E\u043A\u0430\u0437\u0430\u043B\u0438, \u0447\u0442\u043E \u043B\u044E\u0431\u0430\u044F \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0440\u0430\u0437\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0434\u043B\u0438\u043D\u044B \u043D\u0435 \u043C\u0435\u043D\u0435\u0435 (r-1)(s-1)+1 \u0441\u043E\u0434\u0435\u0440\u0436\u0438\u0442 \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0432\u043E\u0437\u0440\u0430\u0441\u0442\u0430\u044E\u0449\u0443\u044E \u043F\u043E\u0434\u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0434\u043B\u0438\u043D\u044B r \u0438\u043B\u0438 \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0443\u0431\u044B\u0432\u0430\u044E\u0449\u0443\u044E \u0434\u043B\u0438\u043D\u044B s. \u0414\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u043E \u043F\u043E\u044F\u0432\u0438\u043B\u043E\u0441\u044C \u0432 \u0442\u043E\u0439 \u0436\u0435 \u0441\u0430\u043C\u043E\u0439 \u0440\u0430\u0431\u043E\u0442\u0435 1935 \u0433\u043E\u0434\u0430, \u0447\u0442\u043E \u0438 \u0437\u0430\u0434\u0430\u0447\u0430 \u0441\u043E \u0441\u0447\u0430\u0441\u0442\u043B\u0438\u0432\u044B\u043C \u043A\u043E\u043D\u0446\u043E\u043C."@ru , "En matem\u00E1ticas, el teorema de Erd\u0151s-Szekeres es un resultado de finitud que precisa uno de los corolarios del teorema de Ramsey. Mientras que el teorema de Ramsey facilita probar que toda sucesi\u00F3n infinita de n\u00FAmeros reales distintos contiene una subsucesi\u00F3n infinita mon\u00F3tonamente creciente o una subsucesi\u00F3n infinita mon\u00F3tonamente decreciente, el resultado que probaron Paul Erd\u0151s y va m\u00E1s all\u00E1. Para , dados, probaron que cualquier sucesi\u00F3n de longitud al menos contiene una subsucesi\u00F3n mon\u00F3tonamente creciente de longitud o una subsucesi\u00F3n mon\u00F3tonamente decreciente de longitud . La demostraci\u00F3n est\u00E1 en el mismo art\u00EDculo de 1935 que menciona el problema del final feliz.\u200B"@es , "\u0423 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456, \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0415\u0440\u0434\u0435\u0448\u0430\u2014\u0421\u0435\u043A\u0435\u0440\u0435\u0448\u0430 \u0454 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u043F\u0440\u043E \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0456 \u043C\u043D\u043E\u0436\u0438\u043D\u0438, \u0449\u043E \u0443\u0442\u043E\u0447\u043D\u044E\u0454 \u043E\u0434\u0438\u043D \u0437 \u043D\u0430\u0441\u043B\u0456\u0434\u043A\u0456\u0432 \u0442\u0435\u043E\u0440\u0435\u043C\u0438 \u0420\u0430\u043C\u0441\u0435\u044F. \u0422\u043E\u0434\u0456 \u044F\u043A \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0420\u0430\u043C\u0441\u0435\u044F \u043F\u043E\u043B\u0435\u0433\u0448\u0443\u0454 \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u044F \u0442\u043E\u0433\u043E, \u0449\u043E \u043A\u043E\u0436\u043D\u0430 \u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C \u0440\u0456\u0437\u043D\u0438\u0445 \u0434\u0456\u0439\u0441\u043D\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u043C\u0456\u0441\u0442\u0438\u0442\u044C \u0430\u0431\u043E \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0437\u0440\u043E\u0441\u0442\u0430\u044E\u0447\u0443 \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0443 \u043F\u0456\u0434\u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C, \u0430\u0431\u043E \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0441\u043F\u0430\u0434\u043D\u0443 \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0443 \u043F\u0456\u0434\u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C, \u0446\u0435\u0439 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442, \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u0438\u0439 \u041F\u0430\u0443\u043B\u0435\u043C \u0415\u0440\u0434\u0435\u0448\u0435\u043C \u0442\u0430 \u0414\u044C\u0439\u043E\u0440\u0434\u0435\u043C \u0421\u0435\u043A\u0435\u0440\u0435\u0448\u0435\u043C \u0456\u0434\u0435 \u0434\u0430\u043B\u0456. \u0414\u043B\u044F \u0434\u0430\u043D\u0438\u0445 r, s \u0432\u043E\u043D\u0438 \u043F\u043E\u043A\u0430\u0437\u0430\u043B\u0438, \u0449\u043E \u0431\u0443\u0434\u044C-\u044F\u043A\u0430 \u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C \u0434\u043E\u0432\u0436\u0438\u043D\u0438 \u043F\u0440\u0438\u043D\u0430\u0439\u043C\u043D\u0456 (r \u2212 1)(s \u2212 1) + 1 \u043C\u0456\u0441\u0442\u0438\u0442\u044C \u0430\u0431\u043E \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0437\u0440\u043E\u0441\u0442\u0430\u044E\u0447\u0443 \u043F\u0456\u0434\u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C \u0434\u043E\u0432\u0436\u0438\u043D\u0438 r, \u0430\u0431\u043E \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0441\u043F\u0430\u0434\u043D\u0443 \u0434\u043E\u0432\u0436\u0438\u043D\u0438 s. \u0414\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u044F \u0437'\u044F\u0432\u0438\u043B\u043E\u0441\u044F \u0443 \u0442\u043E\u0439 \u0441\u0430\u043C\u0456\u0439 \u0440\u043E\u0431\u043E\u0442\u0456 1935 \u0440\u043E\u043A\u0443, \u0449\u043E \u0439 ."@uk , "En math\u00E9matiques, et notamment en g\u00E9om\u00E9trie discr\u00E8te, le th\u00E9or\u00E8me d'Erd\u0151s-Szekeres est une version finitaire d'un corollaire du th\u00E9or\u00E8me de Ramsey. Alors que le th\u00E9or\u00E8me de Ramsey permet de prouver facilement que toute suite infinie de r\u00E9els distincts contient au moins une sous-suite infinie croissante ou une sous-suite infinie d\u00E9croissante, le r\u00E9sultat prouv\u00E9 par Paul Erd\u0151s et George Szekeres est plus pr\u00E9cis en donnant des bornes sur les longueurs des suites. L'\u00E9nonc\u00E9 est le suivant : Dans le m\u00EAme article de 1935 o\u00F9 ce r\u00E9sultat est d\u00E9montr\u00E9 figure aussi le Happy Ending problem."@fr ; foaf:depiction <http://commons.wikimedia.org/wiki/Special:FilePath/Monotone-subseq-17-5.svg> . @prefix dcterms: <http://purl.org/dc/terms/> . @prefix dbc: <http://dbpedia.org/resource/Category:> . <http://dbpedia.org/resource/Erd\u0151s\u2013Szekeres_theorem> dcterms:subject dbc:Theorems_in_discrete_mathematics , <http://dbpedia.org/resource/Category:Paul_Erd\u0151s> , dbc:Permutation_patterns , dbc:Articles_containing_proofs , dbc:Ramsey_theory , dbc:Theorems_in_discrete_geometry ; dbo:abstract "\u0641\u064A \u0627\u0644\u0631\u064A\u0627\u0636\u064A\u0627\u062A\u060C \u062A\u0646\u0635 \u0645\u0628\u0631\u0647\u0646\u0629 \u0625\u064A\u0631\u062F\u0648\u0633-\u0633\u064A\u0643\u0631\u064A\u0633 \u0639\u0644\u0649 \u0623\u0646\u0647 \u0641\u064A \u0643\u0644 \u0645\u062A\u062A\u0627\u0644\u064A\u0629 \u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u0623\u0639\u062F\u0627\u062F \u062D\u0642\u064A\u0642\u064A\u0629 \u0628\u0637\u0648\u0644 \u060C \u064A\u0648\u062C\u062F \u0644\u0647\u0627 \u0645\u062A\u062A\u0627\u0644\u064A\u0629 \u062C\u0632\u0626\u064A\u0629 \u0645\u062A\u0632\u0627\u064A\u062F\u0629 \u0628\u0637\u0648\u0644 \u0623\u0648 \u0645\u062A\u062A\u0627\u0644\u064A\u0629 \u062C\u0632\u0626\u064A\u0629 \u0645\u062A\u0646\u0627\u0642\u0635\u0629 \u0628\u0637\u0648\u0644 . \u0647\u0630\u0647 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0647\u064A \u0645\u0628\u0631\u0647\u0646\u0629 \u0645\u062B\u0627\u0644\u064A\u0629 \u0641\u064A \u0646\u0638\u0631\u064A\u0629 \u0631\u0645\u0632\u064A\u060C \u0627\u0644\u062A\u064A \u062A\u0628\u062D\u062B \u0627\u0644\u0627\u0646\u062A\u0638\u0627\u0645 \u0648\u0633\u0637 \u0627\u0644\u0641\u0648\u0636\u0649. \u062A\u0645\u062A \u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629 \u0639\u0644\u0649 \u064A\u062F \u0628\u0648\u0644 \u0625\u064A\u0631\u062F\u0648\u0633 \u0641\u064A \u0645\u0642\u0627\u0644 \u0644\u0647\u0645\u0627 \u0633\u0646\u0629 1935."@ar , "\u0423 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0446\u0456, \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0415\u0440\u0434\u0435\u0448\u0430\u2014\u0421\u0435\u043A\u0435\u0440\u0435\u0448\u0430 \u0454 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442 \u043F\u0440\u043E \u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0456 \u043C\u043D\u043E\u0436\u0438\u043D\u0438, \u0449\u043E \u0443\u0442\u043E\u0447\u043D\u044E\u0454 \u043E\u0434\u0438\u043D \u0437 \u043D\u0430\u0441\u043B\u0456\u0434\u043A\u0456\u0432 \u0442\u0435\u043E\u0440\u0435\u043C\u0438 \u0420\u0430\u043C\u0441\u0435\u044F. \u0422\u043E\u0434\u0456 \u044F\u043A \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0420\u0430\u043C\u0441\u0435\u044F \u043F\u043E\u043B\u0435\u0433\u0448\u0443\u0454 \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u044F \u0442\u043E\u0433\u043E, \u0449\u043E \u043A\u043E\u0436\u043D\u0430 \u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C \u0440\u0456\u0437\u043D\u0438\u0445 \u0434\u0456\u0439\u0441\u043D\u0438\u0445 \u0447\u0438\u0441\u0435\u043B \u043C\u0456\u0441\u0442\u0438\u0442\u044C \u0430\u0431\u043E \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0437\u0440\u043E\u0441\u0442\u0430\u044E\u0447\u0443 \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0443 \u043F\u0456\u0434\u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C, \u0430\u0431\u043E \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0441\u043F\u0430\u0434\u043D\u0443 \u043D\u0435\u0441\u043A\u0456\u043D\u0447\u0435\u043D\u043D\u0443 \u043F\u0456\u0434\u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C, \u0446\u0435\u0439 \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442, \u0434\u043E\u0432\u0435\u0434\u0435\u043D\u0438\u0439 \u041F\u0430\u0443\u043B\u0435\u043C \u0415\u0440\u0434\u0435\u0448\u0435\u043C \u0442\u0430 \u0414\u044C\u0439\u043E\u0440\u0434\u0435\u043C \u0421\u0435\u043A\u0435\u0440\u0435\u0448\u0435\u043C \u0456\u0434\u0435 \u0434\u0430\u043B\u0456. \u0414\u043B\u044F \u0434\u0430\u043D\u0438\u0445 r, s \u0432\u043E\u043D\u0438 \u043F\u043E\u043A\u0430\u0437\u0430\u043B\u0438, \u0449\u043E \u0431\u0443\u0434\u044C-\u044F\u043A\u0430 \u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C \u0434\u043E\u0432\u0436\u0438\u043D\u0438 \u043F\u0440\u0438\u043D\u0430\u0439\u043C\u043D\u0456 (r \u2212 1)(s \u2212 1) + 1 \u043C\u0456\u0441\u0442\u0438\u0442\u044C \u0430\u0431\u043E \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0437\u0440\u043E\u0441\u0442\u0430\u044E\u0447\u0443 \u043F\u0456\u0434\u043F\u043E\u0441\u043B\u0456\u0434\u043E\u0432\u043D\u0456\u0441\u0442\u044C \u0434\u043E\u0432\u0436\u0438\u043D\u0438 r, \u0430\u0431\u043E \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0441\u043F\u0430\u0434\u043D\u0443 \u0434\u043E\u0432\u0436\u0438\u043D\u0438 s. \u0414\u043E\u0432\u0435\u0434\u0435\u043D\u043D\u044F \u0437'\u044F\u0432\u0438\u043B\u043E\u0441\u044F \u0443 \u0442\u043E\u0439 \u0441\u0430\u043C\u0456\u0439 \u0440\u043E\u0431\u043E\u0442\u0456 1935 \u0440\u043E\u043A\u0443, \u0449\u043E \u0439 ."@uk , "\uC218\uD559\uC5D0\uC11C \uC5D0\uB974\uB418\uC2DC-\uC138\uCF00\uB808\uC2DC \uC815\uB9AC\uB294 \uC8FC\uC5B4\uC9C4 , \uC5D0 \uB300\uD574 \uAE38\uC774\uAC00 \uC774\uC0C1\uC778 \uC11C\uB85C \uB2E4\uB978 \uC2E4\uC218\uB4E4\uC758 \uC218\uC5F4\uC740 \uAE38\uC774 \uC758 \uB2E8\uC870 \uC99D\uAC00\uD558\uB294 \uBD80\uBD84\uC218\uC5F4 \uB610\uB294 \uAE38\uC774 \uC758 \uB2E8\uC870 \uAC10\uC18C\uD558\uB294 \uBD80\uBD84\uC218\uC5F4\uC744 \uD3EC\uD568\uD55C\uB2E4\uB294 \uC815\uB9AC\uC774\uB2E4. \uC99D\uBA85\uC740 \uD574\uD53C \uC5D4\uB529 \uBB38\uC81C\uB97C \uC5B8\uAE09\uD55C \uB3D9\uC77C\uD55C 1935\uB144 \uB17C\uBB38\uC5D0 \uB098\uD0C0\uB0AC\uB2E4. \uC5D0\uB974\uB418\uC2DC-\uC138\uCF00\uB808\uC2DC \uC815\uB9AC\uB294 \uC815\uD655\uD788 \uB7A8\uC9C0\uC758 \uC815\uB9AC\uC758 \uB530\uB984\uC815\uB9AC\uAC00 \uB418\uB294 \uC720\uD55C\uD55C \uACB0\uACFC \uC911 \uD558\uB098\uC774\uB2E4. \uB7A8\uC9C0\uC758 \uC815\uB9AC\uB97C \uC0AC\uC6A9\uD558\uBA74 \uBAA8\uB4E0 \uC11C\uB85C \uB2E4\uB978 \uC2E4\uC218\uB85C \uC774\uB8E8\uC5B4\uC9C4 \uBB34\uD55C \uC218\uC5F4\uC774 \uB2E8\uC870 \uC99D\uAC00\uD558\uB294 \uBB34\uD55C \uBD80\uBD84 \uC218\uC5F4 \uB610\uB294 \uB2E8\uC870 \uAC10\uC18C\uD558\uB294 \uBB34\uD55C \uBD80\uBD84 \uC218\uC5F4\uC744 \uD3EC\uD568\uD55C\uB2E4\uB294 \uAC83\uC744 \uC27D\uAC8C \uC99D\uBA85\uD560 \uC218 \uC788\uC9C0\uB9CC \uC5D0\uB974\uB418\uC2DC \uD314\uACFC \uC138\uCF00\uB808\uC2DC \uC8C4\uB974\uC9C0\uAC00 \uC99D\uBA85\uD55C \uACB0\uACFC\uB294 \uB354 \uB098\uC544\uAC04\uB2E4."@ko , "En matem\u00E1ticas, el teorema de Erd\u0151s-Szekeres es un resultado de finitud que precisa uno de los corolarios del teorema de Ramsey. Mientras que el teorema de Ramsey facilita probar que toda sucesi\u00F3n infinita de n\u00FAmeros reales distintos contiene una subsucesi\u00F3n infinita mon\u00F3tonamente creciente o una subsucesi\u00F3n infinita mon\u00F3tonamente decreciente, el resultado que probaron Paul Erd\u0151s y va m\u00E1s all\u00E1. Para , dados, probaron que cualquier sucesi\u00F3n de longitud al menos contiene una subsucesi\u00F3n mon\u00F3tonamente creciente de longitud o una subsucesi\u00F3n mon\u00F3tonamente decreciente de longitud . La demostraci\u00F3n est\u00E1 en el mismo art\u00EDculo de 1935 que menciona el problema del final feliz.\u200B"@es , "In mathematics, the Erd\u0151s\u2013Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r \u2212 1)(s \u2212 1) + 1 contains a monotonically increasing subsequence of length r or a monotonically decreasing subsequence of length s. The proof appeared in the same 1935 paper that mentions the Happy Ending problem. It is a finitary result that makes precise one of the corollaries of Ramsey's theorem. While Ramsey's theorem makes it easy to prove that every infinite sequence of distinct real numbers contains a monotonically increasing infinite subsequence or a monotonically decreasing infinite subsequence, the result proved by Paul Erd\u0151s and George Szekeres goes further."@en , "\u0422\u0435\u043E\u0440\u0435\u043C\u0430 \u042D\u0301\u0440\u0434\u0451\u0448\u0430 \u2014 \u0421\u0435\u0301\u043A\u0435\u0440\u0435\u0448\u0430 \u0432 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0435 \u2014 \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043D\u0438\u0435, \u0443\u0442\u043E\u0447\u043D\u044F\u044E\u0449\u0435\u0435 \u043E\u0434\u043D\u043E \u0438\u0437 \u0441\u043B\u0435\u0434\u0441\u0442\u0432\u0438\u0439 \u0442\u0435\u043E\u0440\u0435\u043C\u044B \u0420\u0430\u043C\u0441\u0435\u044F \u0434\u043B\u044F \u0444\u0438\u043D\u0438\u0442\u043D\u043E\u0433\u043E \u0441\u043B\u0443\u0447\u0430\u044F. \u0412 \u0442\u043E \u0432\u0440\u0435\u043C\u044F \u043A\u0430\u043A \u0442\u0435\u043E\u0440\u0435\u043C\u0430 \u0420\u0430\u043C\u0441\u0435\u044F \u043E\u0431\u043B\u0435\u0433\u0447\u0430\u0435\u0442 \u0434\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u043E \u0442\u043E\u0433\u043E, \u0447\u0442\u043E \u043A\u0430\u0436\u0434\u0430\u044F \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0440\u0430\u0437\u043D\u044B\u0445 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043B\u044C\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0441\u043E\u0434\u0435\u0440\u0436\u0438\u0442 \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0432\u043E\u0437\u0440\u0430\u0441\u0442\u0430\u044E\u0449\u0443\u044E \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u0443\u044E \u043F\u043E\u0434\u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0438\u043B\u0438 \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0443\u0431\u044B\u0432\u0430\u044E\u0449\u0443\u044E \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u0443\u044E \u043F\u043E\u0434\u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C, \u0440\u0435\u0437\u0443\u043B\u044C\u0442\u0430\u0442, \u0434\u043E\u043A\u0430\u0437\u0430\u043D\u043D\u044B\u0439 \u041F\u0430\u043B\u043E\u043C \u042D\u0440\u0434\u0451\u0448\u0435\u043C \u0438 \u0414\u044C\u0451\u0440\u0434\u0435\u043C \u0421\u0435\u043A\u0435\u0440\u0435\u0448\u0435\u043C, \u0438\u0434\u0451\u0442 \u0434\u0430\u043B\u044C\u0448\u0435. \u0414\u043B\u044F \u0434\u0430\u043D\u043D\u044B\u0445 r, s \u043E\u043D\u0438 \u043F\u043E\u043A\u0430\u0437\u0430\u043B\u0438, \u0447\u0442\u043E \u043B\u044E\u0431\u0430\u044F \u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0440\u0430\u0437\u043D\u044B\u0445 \u0447\u0438\u0441\u0435\u043B \u0434\u043B\u0438\u043D\u044B \u043D\u0435 \u043C\u0435\u043D\u0435\u0435 (r-1)(s-1)+1 \u0441\u043E\u0434\u0435\u0440\u0436\u0438\u0442 \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0432\u043E\u0437\u0440\u0430\u0441\u0442\u0430\u044E\u0449\u0443\u044E \u043F\u043E\u0434\u043F\u043E\u0441\u043B\u0435\u0434\u043E\u0432\u0430\u0442\u0435\u043B\u044C\u043D\u043E\u0441\u0442\u044C \u0434\u043B\u0438\u043D\u044B r \u0438\u043B\u0438 \u043C\u043E\u043D\u043E\u0442\u043E\u043D\u043D\u043E \u0443\u0431\u044B\u0432\u0430\u044E\u0449\u0443\u044E \u0434\u043B\u0438\u043D\u044B s. \u0414\u043E\u043A\u0430\u0437\u0430\u0442\u0435\u043B\u044C\u0441\u0442\u0432\u043E \u043F\u043E\u044F\u0432\u0438\u043B\u043E\u0441\u044C \u0432 \u0442\u043E\u0439 \u0436\u0435 \u0441\u0430\u043C\u043E\u0439 \u0440\u0430\u0431\u043E\u0442\u0435 1935 \u0433\u043E\u0434\u0430, \u0447\u0442\u043E \u0438 \u0437\u0430\u0434\u0430\u0447\u0430 \u0441\u043E \u0441\u0447\u0430\u0441\u0442\u043B\u0438\u0432\u044B\u043C \u043A\u043E\u043D\u0446\u043E\u043C."@ru , "En math\u00E9matiques, et notamment en g\u00E9om\u00E9trie discr\u00E8te, le th\u00E9or\u00E8me d'Erd\u0151s-Szekeres est une version finitaire d'un corollaire du th\u00E9or\u00E8me de Ramsey. Alors que le th\u00E9or\u00E8me de Ramsey permet de prouver facilement que toute suite infinie de r\u00E9els distincts contient au moins une sous-suite infinie croissante ou une sous-suite infinie d\u00E9croissante, le r\u00E9sultat prouv\u00E9 par Paul Erd\u0151s et George Szekeres est plus pr\u00E9cis en donnant des bornes sur les longueurs des suites. L'\u00E9nonc\u00E9 est le suivant : Soient r et s deux entiers. Toute suite d'au moins (r \u2013 1)(s \u2013 1) + 1 nombres r\u00E9els contient une sous-suite croissante de longueur r ou une sous-suite d\u00E9croissante de longueur s. Dans le m\u00EAme article de 1935 o\u00F9 ce r\u00E9sultat est d\u00E9montr\u00E9 figure aussi le Happy Ending problem."@fr ; dbo:wikiPageWikiLink dbr:Young_tableau , dbr:Antichain , dbr:Happy_Ending_problem , dbc:Theorems_in_discrete_geometry , dbr:Subsequence , <http://dbpedia.org/resource/Mirsky\u0027s_theorem> , <http://dbpedia.org/resource/File:Monotone-subseq-17-5.svg> , dbc:Permutation_patterns , dbr:Pigeonhole_principle , <http://dbpedia.org/resource/Ramsey\u0027s_theorem> , dbr:Mathematics , dbc:Articles_containing_proofs , dbr:Permutation_pattern , dbc:Ramsey_theory , dbr:Longest_increasing_subsequence_problem , <http://dbpedia.org/resource/Robinson\u2013Schensted_correspondence> , dbr:George_Szekeres , dbc:Theorems_in_discrete_mathematics , <http://dbpedia.org/resource/Category:Paul_Erd\u0151s> , <http://dbpedia.org/resource/Paul_Erd\u0151s> , dbr:Polygonal_path , <http://dbpedia.org/resource/Dilworth\u0027s_theorem> , dbr:Euclidean_plane . @prefix dbp: <http://dbpedia.org/property/> . @prefix dbt: <http://dbpedia.org/resource/Template:> . <http://dbpedia.org/resource/Erd\u0151s\u2013Szekeres_theorem> dbp:wikiPageUsesTemplate dbt:Harvtxt , dbt:Reflist , dbt:Radic , dbt:Mathworld , dbt:Short_description ; 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