Matches in SemOpenAlex for { <https://semopenalex.org/work/W2040673954> ?p ?o ?g. }
Showing items 1 to 72 of
72
with 100 items per page.
- W2040673954 abstract "A famous theorem by van der Waerden states the following: Given any finite coloring of the integers, one color contains arbitrarily long arithmetic progressions. Equivalently, for every q,k, there is an N = N(q,k) such that for every q-coloring of an interval of length N one color contains a progression of length k. An obvious question is what is the growth rate of N = N(q,k). Some proofs, like van der Waerden's combinatorial argument, answer this question directly, while the topological proof by Furstenberg and Weiss does not. We present an analysis of (Girard's variant of) Furstenberg and Weiss's proof based on monotone functional interpretation, both yielding bounds and providing a general illustration of proof mining in topological dynamics. The bounds do not improve previous results by Girard, but only—as is also revealed by the analysis—because the combinatorial proof and the topological dynamics proof in principle are identical." @default.
- W2040673954 created "2016-06-24" @default.
- W2040673954 creator A5026223848 @default.
- W2040673954 date "2008-10-01" @default.
- W2040673954 modified "2023-09-25" @default.
- W2040673954 title "Proof Mining in Topological Dynamics" @default.
- W2040673954 cites W1022649828 @default.
- W2040673954 cites W1511662047 @default.
- W2040673954 cites W1549382427 @default.
- W2040673954 cites W1608607427 @default.
- W2040673954 cites W1893170605 @default.
- W2040673954 cites W1970366772 @default.
- W2040673954 cites W2026998787 @default.
- W2040673954 cites W2037221615 @default.
- W2040673954 cites W2335400162 @default.
- W2040673954 cites W4212782960 @default.
- W2040673954 cites W654183047 @default.
- W2040673954 doi "https://doi.org/10.1215/00294527-2008-022" @default.
- W2040673954 hasPublicationYear "2008" @default.
- W2040673954 type Work @default.
- W2040673954 sameAs 2040673954 @default.
- W2040673954 citedByCount "15" @default.
- W2040673954 countsByYear W20406739542012 @default.
- W2040673954 countsByYear W20406739542014 @default.
- W2040673954 countsByYear W20406739542016 @default.
- W2040673954 countsByYear W20406739542017 @default.
- W2040673954 countsByYear W20406739542018 @default.
- W2040673954 countsByYear W20406739542019 @default.
- W2040673954 countsByYear W20406739542021 @default.
- W2040673954 countsByYear W20406739542022 @default.
- W2040673954 crossrefType "journal-article" @default.
- W2040673954 hasAuthorship W2040673954A5026223848 @default.
- W2040673954 hasBestOaLocation W20406739541 @default.
- W2040673954 hasConcept C108710211 @default.
- W2040673954 hasConcept C112291201 @default.
- W2040673954 hasConcept C114614502 @default.
- W2040673954 hasConcept C116493835 @default.
- W2040673954 hasConcept C118539577 @default.
- W2040673954 hasConcept C118615104 @default.
- W2040673954 hasConcept C135754263 @default.
- W2040673954 hasConcept C2524010 @default.
- W2040673954 hasConcept C2834757 @default.
- W2040673954 hasConcept C33923547 @default.
- W2040673954 hasConceptScore W2040673954C108710211 @default.
- W2040673954 hasConceptScore W2040673954C112291201 @default.
- W2040673954 hasConceptScore W2040673954C114614502 @default.
- W2040673954 hasConceptScore W2040673954C116493835 @default.
- W2040673954 hasConceptScore W2040673954C118539577 @default.
- W2040673954 hasConceptScore W2040673954C118615104 @default.
- W2040673954 hasConceptScore W2040673954C135754263 @default.
- W2040673954 hasConceptScore W2040673954C2524010 @default.
- W2040673954 hasConceptScore W2040673954C2834757 @default.
- W2040673954 hasConceptScore W2040673954C33923547 @default.
- W2040673954 hasIssue "4" @default.
- W2040673954 hasLocation W20406739541 @default.
- W2040673954 hasOpenAccess W2040673954 @default.
- W2040673954 hasPrimaryLocation W20406739541 @default.
- W2040673954 hasRelatedWork W2001480748 @default.
- W2040673954 hasRelatedWork W2032915363 @default.
- W2040673954 hasRelatedWork W2040673954 @default.
- W2040673954 hasRelatedWork W2155085907 @default.
- W2040673954 hasRelatedWork W2461509449 @default.
- W2040673954 hasRelatedWork W2602353158 @default.
- W2040673954 hasRelatedWork W2736121670 @default.
- W2040673954 hasRelatedWork W2964038337 @default.
- W2040673954 hasRelatedWork W4293877181 @default.
- W2040673954 hasRelatedWork W4302380128 @default.
- W2040673954 hasVolume "49" @default.
- W2040673954 isParatext "false" @default.
- W2040673954 isRetracted "false" @default.
- W2040673954 magId "2040673954" @default.
- W2040673954 workType "article" @default.