Geodesic
Estimates for Cameron--Erd\H os constants
Diskretnaya Matematika, Tome 18 (2006) no. 2, pp. 55-70.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DM_2006_18_2_a3,
     author = {K. G. Omel'yanov},
     title = {Estimates for {Cameron--Erd\H} os constants},
     journal = {Diskretnaya Matematika},
     pages = {55--70},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2006_18_2_a3/}
}
TY  - JOUR
AU  - K. G. Omel'yanov
TI  - Estimates for Cameron--Erd\H os constants
JO  - Diskretnaya Matematika
PY  - 2006
SP  - 55
EP  - 70
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2006_18_2_a3/
LA  - ru
ID  - DM_2006_18_2_a3
ER  - 
%0 Journal Article
%A K. G. Omel'yanov
%T Estimates for Cameron--Erd\H os constants
%J Diskretnaya Matematika
%D 2006
%P 55-70
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2006_18_2_a3/
%G ru
%F DM_2006_18_2_a3
K. G. Omel'yanov. Estimates for Cameron--Erd\H os constants. Diskretnaya Matematika, Tome 18 (2006) no. 2, pp. 55-70. http://geodesic.mathdoc.fr/item/DM_2006_18_2_a3/

[1] Cameron P., Erdos P., “On the number of integers with various properties”, Number theory, Proc. First Conf. Canadian Number Theory Ass., de Gruyter, Berlin, 1990, 61–79

[2] Sapozhenko A. A., “Dokazatelstvo gipotezy Kamerona–Erdesha o chisle mnozhestv, svobodnykh ot summ”, Matem. voprosy kibern., 12 (2003), 5–14

[3] Alon N., “Independent sets in regular graphs and sum-free subsets of finite groups”, Israel J. Math., 73:2 (1991), 247–256 | DOI | MR | Zbl

[4] Calkin N., “On the number of sum-free sets”, Bull. London Math. Soc., 22 (1990), 141–144 | DOI | MR | Zbl

[5] Lev V. F., Luczak T., Schoen T., “Sum-free sets in abelian groups”, Israel J. Math., 125 (2001), 347–367 | DOI | MR | Zbl

[6] Sapozhenko A. A., “O chisle mnozhestv, svobodnykh ot summ v abelevykh gruppakh”, Vestnik Moskovskogo univ., Ser. 1, Matematika, Mekhanika, 2001, 56–62 ; 2002, 14–18 | MR | Zbl | MR | Zbl

[7] Omelyanov K. G., Sapozhenko A. A., “O chisle mnozhestv, svobodnykh ot summ, v otrezke naturalnykh chisel”, Diskretnaya matematika, 14:3 (2002), 3–7 | MR

[8] Omelyanov K. G., Sapozhenko A. A., “O chisle i strukture mnozhestv, svobodnykh ot summ, v otrezke naturalnykh chisel”, Diskretnaya matematika, 15:4 (2003), 141–147 | MR

[9] Green B., “The Cameron–Erdos conjecture”, Bull. London Math. Soc., 36 (2004), 769–778 | DOI | MR | Zbl

[10] Freiman G. A., “Slozhenie konechnykh mnozhestv”, Izv. VUZov, Matematika, 1959, no. 6(13), 202–213 | MR | Zbl

[11] Omelyanov K. G., “O chisle nezavisimykh mnozhestv v povrezhdennykh grafakh Keli”, Diskretnaya matematika, 17:3 (2005), 105–108 | MR | Zbl