RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2011, Volume 75, Issue 5, Pages 195–224 (Mi izv4270)  

This article is cited in 2 scientific papers (total in 2 papers)

Van der Waerden's function and colourings of hypergraphs

D. A. Shabanov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

DOI: https://doi.org/10.4213/im4270

Full text: PDF file (659 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2011, 75:5, 1063–1091

Bibliographic databases:

Document Type: Article
UDC: 511.218+519.112.4+519.212.2
MSC: 05C15, 05C65, 05D40, 11B75
Received: 09.12.2009

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
\Bibitem{Sha11}
\by D.~A.~Shabanov
\paper Van der Waerden's function and colourings of hypergraphs
\jour Izv. RAN. Ser. Mat.
\yr 2011
\vol 75
\issue 5
\pages 195--224
\mathnet{http://mi.mathnet.ru/izv4270}
\crossref{https://doi.org/10.4213/im4270}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2884668}
\zmath{https://zbmath.org/?q=an:1246.05060}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2011IzMat..75.1063S}
\elib{http://elibrary.ru/item.asp?id=20358815}
\transl
\jour Izv. Math.
\yr 2011
\vol 75
\issue 5
\pages 1063--1091
\crossref{https://doi.org/10.1070/IM2011v075n05ABEH002564}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000296665700009}
\elib{http://elibrary.ru/item.asp?id=18012437}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80555138829}


Linking options:
  • http://mi.mathnet.ru/eng/izv4270
  • https://doi.org/10.4213/im4270
  • http://mi.mathnet.ru/eng/izv/v75/i5/p195

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Raigorodskii, D. A. Shabanov, “The Erdős–Hajnal problem of hypergraph colouring, its generalizations, and related problems”, Russian Math. Surveys, 66:5 (2011), 933–1002  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Shabanov D.A., “Funktsiya Van-der-Vardena i raskraski gipergrafov s bolshim obkhvatom”, Dokl. RAN, 451:6 (2013), 620–620  zmath  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:451
    Full text:58
    References:34
    First page:18

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017