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Izvestiya: Mathematics, 2011, Volume 75, Issue 5, Pages 1063–1091
DOI: https://doi.org/10.1070/IM2011v075n05ABEH002564 (Mi im4270) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Van der Waerden's function and colourings of hypergraphs

D. A. Shabanov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (424 kB) Citations (4) Russian version article
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DOI: https://doi.org/10.1070/IM2011v075n05ABEH002564
Abstract: A classical problem of combinatorial number theory is to compute van der Waerden's function $W(n,r)$. Using random colourings of hypergraphs, we get a new asymptotic lower bound for $W(n,r)$ which improves previous results for a wide range of values of $n$ and $r$.
Keywords: van der Waerden's theorem, arithmetic progressions, hypergraph, chromatic number.
Received: 09.12.2009
Bibliographic databases:
Document Type: Article
UDC: 511.218+519.112.4+519.212.2
MSC: 05C15, 05C65, 05D40, 11B75
Language: English
Original paper language: Russian
Citation: D. A. Shabanov, “Van der Waerden's function and colourings of hypergraphs”, Izv. Math., 75:5 (2011), 1063–1091
Citation in format AMSBIB
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\paper Van der Waerden's function and colourings of hypergraphs
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\yr 2011
\vol 75
\issue 5
\pages 1063--1091
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  • https://doi.org/10.1070/IM2011v075n05ABEH002564
  • https://www.mathnet.ru/eng/im/v75/i5/p195
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:993
    Russian version PDF:325
    English version PDF:19
    References:84
    First page:18
     
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