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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)
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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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2011, Volume 75, Issue 5, Pages 195–224
DOI: https://doi.org/10.4213/im4270
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. RAN. Ser. Mat., 75:5 (2011), 195–224; Izv. Math., 75:5 (2011), 1063–1091
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:70
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