TY - JOUR

T1 - The number of additive triples in subsets of abelian groups

AU - Samotij, Wojciech

AU - Sudakov, Benny

N1 - Publisher Copyright: Copyright © Cambridge Philosophical Society 2016.

PY - 2016/5/1

Y1 - 2016/5/1

N2 - A set of elements of a finite abelian group is called sum-free if it contains no Schur triple, i.e., no triple of elements x, y, z with x + y = z. The study of how large the largest sum-free subset of a given abelian group is had started more than thirty years before it was finally resolved by Green and Ruzsa a decade ago. We address the following more general question. Suppose that a set A of elements of an abelian group G has cardinality a. How many Schur triples must A contain? Moreover, which sets of a elements of G have the smallest number of Schur triples? In this paper, we answer these questions for various groups G and ranges of a.

AB - A set of elements of a finite abelian group is called sum-free if it contains no Schur triple, i.e., no triple of elements x, y, z with x + y = z. The study of how large the largest sum-free subset of a given abelian group is had started more than thirty years before it was finally resolved by Green and Ruzsa a decade ago. We address the following more general question. Suppose that a set A of elements of an abelian group G has cardinality a. How many Schur triples must A contain? Moreover, which sets of a elements of G have the smallest number of Schur triples? In this paper, we answer these questions for various groups G and ranges of a.

UR - http://www.scopus.com/inward/record.url?scp=84955560339&partnerID=8YFLogxK

U2 - https://doi.org/10.1017/S0305004115000821

DO - https://doi.org/10.1017/S0305004115000821

M3 - مقالة

SN - 0305-0041

VL - 160

SP - 495

EP - 512

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -