TY - JOUR

T1 - Random sum-free subsets of abelian groups

AU - Balogh, József

AU - Morris, Robert

AU - Samotij, Wojciech

N1 - Funding Information:
∗ Research supported in part by: (JB) NSF CAREER Grant DMS-0745185, UIUC Campus Research Board Grants 09072 and 11067, and OTKA Grant K76099; (RM) ERC Advanced grant DMMCA, and a Research Fellowship from Murray Ed-wards College, Cambridge; (WS) Parker Fellowship and Schark Fellowship (from UIUC Mathematics Department) and ERC Advanced Grant DMMCA. Received March 10, 2011 and in revised form November 15, 2012
Publisher Copyright:
© 2014, Hebrew University Magnes Press.

PY - 2014/3/1

Y1 - 2014/3/1

N2 - We characterize the structure of maximum-size sum-free subsets of a random subset of an abelian group G. In particular, we determine the threshold above which, with high probability as |G| → ∞, each such subset is contained in some maximum-size sum-free subset of G, whenever q divides |G| for some (fixed) prime q with q ≡ 2 (mod 3). Moreover, in the special case G = ℤ2n, we determine the sharp threshold for the above property. The proof uses recent ‘transference’ theorems of Conlon and Gowers, together with stability theorems for sum-free sets of abelian groups.

AB - We characterize the structure of maximum-size sum-free subsets of a random subset of an abelian group G. In particular, we determine the threshold above which, with high probability as |G| → ∞, each such subset is contained in some maximum-size sum-free subset of G, whenever q divides |G| for some (fixed) prime q with q ≡ 2 (mod 3). Moreover, in the special case G = ℤ2n, we determine the sharp threshold for the above property. The proof uses recent ‘transference’ theorems of Conlon and Gowers, together with stability theorems for sum-free sets of abelian groups.

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U2 - 10.1007/s11856-013-0071-2

DO - 10.1007/s11856-013-0071-2

M3 - Article

AN - SCOPUS:84886741083

SN - 0021-2172

VL - 199

SP - 651

EP - 685

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -