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About: Erdős–Szekeres theorem
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class="text-nowrap">An Entity of Type: <a href="http://dbpedia.org/class/yago/WikicatTheoremsInCombinatorics">WikicatTheoremsInCombinatorics</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">In mathematics, the Erdős–Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 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.</p> </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Monotone-subseq-17-5.svg?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section> <!-- page-header --> <!-- property-table --> <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ar" >في الرياضيات، تنص مبرهنة إيردوس-سيكريس على أنه في كل متتالية مكونة من أعداد حقيقية بطول ، يوجد لها متتالية جزئية متزايدة بطول أو متتالية جزئية متناقصة بطول . هذه المبرهنة هي مبرهنة مثالية في نظرية رمزي، التي تبحث الانتظام وسط الفوضى. تمت برهنة المبرهنة على يد بول إيردوس في مقال لهما سنة 1935.</span><small> (ar)</small></span></li> <li><span class="literal"><span property="dbo:abstract" lang="en" >In mathematics, the Erdős–Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 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 Erdős and George Szekeres goes further.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="es" >En matemáticas, el teorema de Erdős-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 sucesión infinita de números reales distintos contiene una subsucesión infinita monótonamente creciente o una subsucesión infinita monótonamente decreciente, el resultado que probaron Paul Erdős y va más allá. Para , dados, probaron que cualquier sucesión de longitud al menos contiene una subsucesión monótonamente creciente de longitud o una subsucesión monótonamente decreciente de longitud . La demostración está en el mismo artículo de 1935 que menciona el problema del final feliz.</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="fr" >En mathématiques, et notamment en géométrie discrète, le théorème d'Erdős-Szekeres est une version finitaire d'un corollaire du théorème de Ramsey. Alors que le théorème de Ramsey permet de prouver facilement que toute suite infinie de réels distincts contient au moins une sous-suite infinie croissante ou une sous-suite infinie décroissante, le résultat prouvé par Paul Erdős et George Szekeres est plus précis en donnant des bornes sur les longueurs des suites. L'énoncé est le suivant : Soient r et s deux entiers. Toute suite d'au moins (r – 1)(s – 1) + 1 nombres réels contient une sous-suite croissante de longueur r ou une sous-suite décroissante de longueur s. Dans le même article de 1935 où ce résultat est démontré figure aussi le Happy Ending problem.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ko" >수학에서 에르되시-세케레시 정리는 주어진 , 에 대해 길이가 이상인 서로 다른 실수들의 수열은 길이 의 단조 증가하는 부분수열 또는 길이 의 단조 감소하는 부분수열을 포함한다는 정리이다. 증명은 해피 엔딩 문제를 언급한 동일한 1935년 논문에 나타났다. 에르되시-세케레시 정리는 정확히 램지의 정리의 따름정리가 되는 유한한 결과 중 하나이다. 램지의 정리를 사용하면 모든 서로 다른 실수로 이루어진 무한 수열이 단조 증가하는 무한 부분 수열 또는 단조 감소하는 무한 부분 수열을 포함한다는 것을 쉽게 증명할 수 있지만 에르되시 팔과 세케레시 죄르지가 증명한 결과는 더 나아간다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="uk" >У математиці, теорема Ердеша—Секереша є результат про скінченні множини, що уточнює один з наслідків теореми Рамсея. Тоді як теорема Рамсея полегшує доведення того, що кожна послідовність різних дійсних чисел містить або монотонно зростаючу нескінченну підпослідовність, або монотонно спадну нескінченну підпослідовність, цей результат, доведений Паулем Ердешем та Дьйордем Секерешем іде далі. Для даних r, s вони показали, що будь-яка послідовність довжини принаймні (r − 1)(s − 1) + 1 містить або монотонно зростаючу підпослідовність довжини r, або монотонно спадну довжини s. Доведення з'явилося у той самій роботі 1935 року, що й .</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ru" >Теорема Э́рдёша — Се́кереша в комбинаторике — утверждение, уточняющее одно из следствий теоремы Рамсея для финитного случая. В то время как теорема Рамсея облегчает доказательство того, что каждая последовательность разных действительных чисел содержит монотонно возрастающую бесконечную подпоследовательность или монотонно убывающую бесконечную подпоследовательность, результат, доказанный Палом Эрдёшем и Дьёрдем Секерешем, идёт дальше. Для данных r, s они показали, что любая последовательность разных чисел длины не менее (r-1)(s-1)+1 содержит монотонно возрастающую подпоследовательность длины r или монотонно убывающую длины s. Доказательство появилось в той же самой работе 1935 года, что и задача со счастливым концом.</span><small> (ru)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail"><small>dbo:</small>thumbnail</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/Monotone-subseq-17-5.svg?width=300" href="http://commons.wikimedia.org/wiki/Special:FilePath/Monotone-subseq-17-5.svg?width=300"><small>wiki-commons</small>:Special:FilePath/Monotone-subseq-17-5.svg?width=300</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageID"><small>dbo:</small>wikiPageID</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageID" datatype="xsd:integer" >3115543</span><small> (xsd:integer)</small></span></li> 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class="col-2"><a class="uri" href="http://dbpedia.org/property/urlname"><small>dbp:</small>urlname</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbp:urlname" lang="en" >Erdos-SzekeresTheorem</span><small> (en)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/property/wikiPageUsesTemplate"><small>dbp:</small>wikiPageUsesTemplate</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Harvtxt" href="http://dbpedia.org/resource/Template:Harvtxt"><small>dbt</small>:Harvtxt</a></span></li> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" resource="http://dbpedia.org/resource/Template:Mathworld" href="http://dbpedia.org/resource/Template:Mathworld"><small>dbt</small>:Mathworld</a></span></li> <li><span class="literal"><a class="uri" rel="dbp:wikiPageUsesTemplate" 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جزئية متناقصة بطول . هذه المبرهنة هي مبرهنة مثالية في نظرية رمزي، التي تبحث الانتظام وسط الفوضى. تمت برهنة المبرهنة على يد بول إيردوس في مقال لهما سنة 1935.</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="es" >En matemáticas, el teorema de Erdős-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 sucesión infinita de números reales distintos contiene una subsucesión infinita monótonamente creciente o una subsucesión infinita monótonamente decreciente, el resultado que probaron Paul Erdős y va más allá. Para , dados, probaron que cualquier sucesión de longitud al menos contiene una subsucesión monótonamente creciente de longitud o una subsucesión monótonamente decreciente de longitud . La demostración está en el mismo artículo de 1935 que menciona el problema del final feliz.</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ko" >수학에서 에르되시-세케레시 정리는 주어진 , 에 대해 길이가 이상인 서로 다른 실수들의 수열은 길이 의 단조 증가하는 부분수열 또는 길이 의 단조 감소하는 부분수열을 포함한다는 정리이다. 증명은 해피 엔딩 문제를 언급한 동일한 1935년 논문에 나타났다. 에르되시-세케레시 정리는 정확히 램지의 정리의 따름정리가 되는 유한한 결과 중 하나이다. 램지의 정리를 사용하면 모든 서로 다른 실수로 이루어진 무한 수열이 단조 증가하는 무한 부분 수열 또는 단조 감소하는 무한 부분 수열을 포함한다는 것을 쉽게 증명할 수 있지만 에르되시 팔과 세케레시 죄르지가 증명한 결과는 더 나아간다.</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="uk" >У математиці, теорема Ердеша—Секереша є результат про скінченні множини, що уточнює один з наслідків теореми Рамсея. Тоді як теорема Рамсея полегшує доведення того, що кожна послідовність різних дійсних чисел містить або монотонно зростаючу нескінченну підпослідовність, або монотонно спадну нескінченну підпослідовність, цей результат, доведений Паулем Ердешем та Дьйордем Секерешем іде далі. Для даних r, s вони показали, що будь-яка послідовність довжини принаймні (r − 1)(s − 1) + 1 містить або монотонно зростаючу підпослідовність довжини r, або монотонно спадну довжини s. Доведення з'явилося у той самій роботі 1935 року, що й .</span><small> (uk)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ru" >Теорема Э́рдёша — Се́кереша в комбинаторике — утверждение, уточняющее одно из следствий теоремы Рамсея для финитного случая. В то время как теорема Рамсея облегчает доказательство того, что каждая последовательность разных действительных чисел содержит монотонно возрастающую бесконечную подпоследовательность или монотонно убывающую бесконечную подпоследовательность, результат, доказанный Палом Эрдёшем и Дьёрдем Секерешем, идёт дальше. Для данных r, s они показали, что любая последовательность разных чисел длины не менее (r-1)(s-1)+1 содержит монотонно возрастающую подпоследовательность длины r или монотонно убывающую длины s. Доказательство появилось в той же самой работе 1935 года, что и задача со счастливым концом.</span><small> (ru)</small></span></li> <li><span class="literal"><span property="rdfs:comment" lang="en" >In mathematics, the Erdős–Szekeres theorem asserts that, given r, s, any sequence of distinct real numbers with length at least (r − 1)(s − 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.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="fr" >En mathématiques, et notamment en géométrie discrète, le théorème d'Erdős-Szekeres est une version finitaire d'un corollaire du théorème de Ramsey. Alors que le théorème de Ramsey permet de prouver facilement que toute suite infinie de réels distincts contient au moins une sous-suite infinie croissante ou une sous-suite infinie décroissante, le résultat prouvé par Paul Erdős et George Szekeres est plus précis en donnant des bornes sur les longueurs des suites. L'énoncé est le suivant : Dans le même article de 1935 où ce résultat est démontré figure aussi le Happy Ending problem.</span><small> (fr)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label"><small>rdfs:</small>label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ar" >مبرهنة إيردوس-سيكريس</span><small> (ar)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="es" >Teorema de Erdős-Szekeres</span><small> (es)</small></span></li> <li><span class="literal"><span property="rdfs:label" lang="en" >Erdős–Szekeres theorem</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="fr" >Théorème d'Erdős-Szekeres</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ko" >에르되시-세케레시 정리</span><small> (ko)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="ru" >Теорема Эрдёша — Секереша</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="uk" >Теорема Ердеша — Секереша</span><small> (uk)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs"><small>owl:</small>sameAs</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.08sd1_" href="http://rdf.freebase.com/ns/m.08sd1_"><small>freebase</small>:Erdős–Szekeres theorem</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://www.wikidata.org/entity/Q976607" href="http://www.wikidata.org/entity/Q976607"><small>wikidata</small>:Erdős–Szekeres theorem</a></span></li> <li><span 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