FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2964204159> ?p ?o ?g. }

• W2964204159 endingPage "1053" @default.
• W2964204159 startingPage "1047" @default.
• W2964204159 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E upper S left-parenthesis n right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>S</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>ES(n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the smallest integer such that any set of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E upper S left-parenthesis n right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>S</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>ES(n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> points in the plane in general position contains <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> points in convex position. In their seminal 1935 paper, Erdős and Szekeres showed that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E upper S left-parenthesis n right-parenthesis less-than-or-equal-to StartBinomialOrMatrix 2 n minus 4 Choose n minus 2 EndBinomialOrMatrix plus 1 equals 4 Superscript n minus o left-parenthesis n right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>S</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow> <mml:mstyle scriptlevel=0> <mml:mrow class=MJX-TeXAtom-OPEN> <mml:mo maxsize=1.2em minsize=1.2em>(</mml:mo> </mml:mrow> </mml:mstyle> <mml:mfrac linethickness=0> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>4</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> <mml:mstyle scriptlevel=0> <mml:mrow class=MJX-TeXAtom-CLOSE> <mml:mo maxsize=1.2em minsize=1.2em>)</mml:mo> </mml:mrow> </mml:mstyle> </mml:mrow> </mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>4</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mi>o</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>ES(n) leq {2n - 4choose n-2} + 1 = 4^{n -o(n)}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In 1960, they showed that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E upper S left-parenthesis n right-parenthesis greater-than-or-equal-to 2 Superscript n minus 2 Baseline plus 1> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>S</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>≥<!-- ≥ --></mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo>−<!-- − --></mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>ES(n) geq 2^{n-2} + 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and conjectured this to be optimal. In this paper, we nearly settle the Erdős-Szekeres conjecture by showing that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E upper S left-parenthesis n right-parenthesis equals 2 Superscript n plus o left-parenthesis n right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>S</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> <mml:mi>o</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>ES(n) =2^{n +o(n)}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
• W2964204159 created "2019-07-30" @default.
• W2964204159 creator A5085420480 @default.
• W2964204159 date "2016-09-30" @default.
• W2964204159 modified "2023-09-26" @default.
• W2964204159 title "On the Erdős-Szekeres convex polygon problem" @default.
• W2964204159 cites W1973130400 @default.
• W2964204159 cites W1981259396 @default.
• W2964204159 cites W1990782466 @default.
• W2964204159 cites W2020316116 @default.
• W2964204159 cites W2028140545 @default.
• W2964204159 cites W2044929249 @default.
• W2964204159 cites W2051995105 @default.
• W2964204159 cites W2057647747 @default.
• W2964204159 cites W2068685569 @default.
• W2964204159 cites W2083028555 @default.
• W2964204159 cites W2093184634 @default.
• W2964204159 cites W2167816765 @default.
• W2964204159 cites W2196790641 @default.
• W2964204159 cites W2239826551 @default.
• W2964204159 cites W3098166863 @default.
• W2964204159 cites W3103832364 @default.
• W2964204159 cites W3106160126 @default.
• W2964204159 cites W4210663278 @default.
• W2964204159 cites W4254807835 @default.
• W2964204159 doi "https://doi.org/10.1090/jams/869" @default.
• W2964204159 hasPublicationYear "2016" @default.
• W2964204159 type Work @default.
• W2964204159 sameAs 2964204159 @default.
• W2964204159 citedByCount "30" @default.
• W2964204159 countsByYear W29642041592017 @default.
• W2964204159 countsByYear W29642041592018 @default.
• W2964204159 countsByYear W29642041592019 @default.
• W2964204159 countsByYear W29642041592020 @default.
• W2964204159 countsByYear W29642041592021 @default.
• W2964204159 countsByYear W29642041592022 @default.
• W2964204159 countsByYear W29642041592023 @default.
• W2964204159 crossrefType "journal-article" @default.
• W2964204159 hasAuthorship W2964204159A5085420480 @default.
• W2964204159 hasBestOaLocation W29642041591 @default.
• W2964204159 hasConcept C11413529 @default.
• W2964204159 hasConcept C154945302 @default.
• W2964204159 hasConcept C18903297 @default.
• W2964204159 hasConcept C2777299769 @default.
• W2964204159 hasConcept C33923547 @default.
• W2964204159 hasConcept C41008148 @default.
• W2964204159 hasConcept C86803240 @default.
• W2964204159 hasConceptScore W2964204159C11413529 @default.
• W2964204159 hasConceptScore W2964204159C154945302 @default.
• W2964204159 hasConceptScore W2964204159C18903297 @default.
• W2964204159 hasConceptScore W2964204159C2777299769 @default.
• W2964204159 hasConceptScore W2964204159C33923547 @default.
• W2964204159 hasConceptScore W2964204159C41008148 @default.
• W2964204159 hasConceptScore W2964204159C86803240 @default.
• W2964204159 hasFunder F4320306076 @default.
• W2964204159 hasIssue "4" @default.
• W2964204159 hasLocation W29642041591 @default.
• W2964204159 hasLocation W29642041592 @default.
• W2964204159 hasOpenAccess W2964204159 @default.
• W2964204159 hasPrimaryLocation W29642041591 @default.
• W2964204159 hasRelatedWork W2045715842 @default.
• W2964204159 hasRelatedWork W2089047877 @default.
• W2964204159 hasRelatedWork W2090558690 @default.
• W2964204159 hasRelatedWork W2105880240 @default.
• W2964204159 hasRelatedWork W2349865494 @default.
• W2964204159 hasRelatedWork W2352982982 @default.
• W2964204159 hasRelatedWork W2372553222 @default.
• W2964204159 hasRelatedWork W2925832130 @default.
• W2964204159 hasRelatedWork W3157620392 @default.
• W2964204159 hasRelatedWork W3189264969 @default.
• W2964204159 hasVolume "30" @default.
• W2964204159 isParatext "false" @default.
• W2964204159 isRetracted "false" @default.
• W2964204159 magId "2964204159" @default.
• W2964204159 workType "article" @default.