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 - https://www.scopus.com/pages/publications/84955560339
U2 - 10.1017/S0305004115000821
DO - 10.1017/S0305004115000821
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AN - SCOPUS:84955560339
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 -