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Diskr. Mat., 2006, Volume 18, Issue 2, Pages 55–70 (Mi dm46)  

This article is cited in 3 scientific papers (total in 3 papers)

Estimates for Cameron–Erdős constants

K. G. Omel'yanov


Abstract: A set $B$ of integers is called sum-free if for any $a,b \in B$ the number $a+b$ does not belong to the set $B$. Let $s(n)$ be the number of sum-free sets in the interval of natural numbers $[1,n]$. As shown by Cameron, Erdős, and Sapozhenko, there exist constants $c_0$ and $c_1$ such that $s(n)\sim (c_0+1)2^{\lceil n/2\rceil}$ for even $n$ and $s(n)\sim (c_1+1)2^{\lceil n/2\rceil}$ for odd $n$ tending to infinity. The constants $c_0$ and $c_1$ are usually referred to as the Cameron–Erdős constants. In this paper, we obtain upper and lower bounds for the Cameron–Erdős constants which give the two first decimal places of their exact values.
This research was supported by the Russian Foundation for Basic Research, grant 04–01–00359.

DOI: https://doi.org/10.4213/dm46

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English version:
Discrete Mathematics and Applications, 2006, 16:3, 205–220

Bibliographic databases:

UDC: 519.15
Received: 21.11.2005

Citation: K. G. Omel'yanov, “Estimates for Cameron–Erdős constants”, Diskr. Mat., 18:2 (2006), 55–70; Discrete Math. Appl., 16:3 (2006), 205–220

Citation in format AMSBIB
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\by K.~G.~Omel'yanov
\paper Estimates for Cameron--Erd\H os constants
\jour Diskr. Mat.
\yr 2006
\vol 18
\issue 2
\pages 55--70
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\crossref{https://doi.org/10.4213/dm46}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2283331}
\zmath{https://zbmath.org/?q=an:1128.11010}
\elib{http://elibrary.ru/item.asp?id=9311195}
\transl
\jour Discrete Math. Appl.
\yr 2006
\vol 16
\issue 3
\pages 205--220
\crossref{https://doi.org/10.1515/156939206777970426}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747487036}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Sapozhenko, “O chisle mnozhestv, svobodnykh ot summ”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 151, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2009, 139–146  mathnet
    2. A. A. Sapozhenko, “Solution of the Cameron–Erdős problem for groups of prime order”, Comput. Math. Math. Phys., 49:8 (2009), 1435–1441  mathnet  crossref  zmath  isi
    3. Sapozhenko A. A., “Asymptotics of the number of sum-free sets in groups of prime order”, Dokl. Math., 79:1 (2009), 79–80  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
  • Дискретная математика
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