AbstractWe show that for any set A in a finite Abelian group G that has at least c|A|3 solutions to a1+a2=a3+a4, ai∈A there exist sets A′⊆A and Λ⊆G, Λ={λ1,…,λt}, t≪c−1log|A| such that A′ is contained in {∑j=1tεjλj|εj∈{0,−1,1}} and A′ has ≫c|A|3 solutions to a1′+a2′=a3′+a4′, ai′∈A′. We also study so-called symmetric sets or, in other words, sets of large values of convolution
A subset $\mathcal{A}$ of a finite abelian group $(G,+)$ is called a $B_h$ set on $G$ if all sums of...
AbstractFor a prime p, a subset S of Zp is a sumset if S=A+A for some A⊂Zp. Let f(p) denote the maxi...
We prove the following conjecture of Shkredov and Solymosi: every subset $A \subset \mathbf{Z}^2$ su...
AbstractWe show that for any set A in a finite Abelian group G that has at least c|A|3 solutions to ...
AbstractWe investigate the structure of finite sets A⊆Z where |A+A| is large. We present a combinato...
Let A, B and S be subsets of a finite Abelian group G. The restricted sumset of A and B with respect...
AbstractIn an abelian group G, a more sums than differences (MSTD) set is a subset A⊂G such that |A+...
AbstractA basic problem raised by Kneser was to describe all the finite subsets A, B of an abelian g...
AbstractLet G be a finite abelian group with a ‘sufficiently small’ proportion of elements of order ...
AbstractLet G≃Z/k1Z⊕⋯⊕Z/kNZ be a finite abelian group with ki|ki−1(2≤i≤N). For a matrix Y=(ai,j)∈ZR×...
AbstractGiven a finite abelian group G (written additively), and a subset S of G, the size r(S) of t...
This article has been retracted at the request of the Editor-in-Chief and author. Please see http://...
The Balog-Szemerédi-Gowers theorem has a rich history, and is a very useful tool in additive combin...
AbstractLet A be a set of k⩾5 elements of an Abelian group G in which the order of the smallest nonz...
Let G be a finite Abelian group and A a subset of G. The spectrum of A is the set of its large Fouri...
A subset $\mathcal{A}$ of a finite abelian group $(G,+)$ is called a $B_h$ set on $G$ if all sums of...
AbstractFor a prime p, a subset S of Zp is a sumset if S=A+A for some A⊂Zp. Let f(p) denote the maxi...
We prove the following conjecture of Shkredov and Solymosi: every subset $A \subset \mathbf{Z}^2$ su...
AbstractWe show that for any set A in a finite Abelian group G that has at least c|A|3 solutions to ...
AbstractWe investigate the structure of finite sets A⊆Z where |A+A| is large. We present a combinato...
Let A, B and S be subsets of a finite Abelian group G. The restricted sumset of A and B with respect...
AbstractIn an abelian group G, a more sums than differences (MSTD) set is a subset A⊂G such that |A+...
AbstractA basic problem raised by Kneser was to describe all the finite subsets A, B of an abelian g...
AbstractLet G be a finite abelian group with a ‘sufficiently small’ proportion of elements of order ...
AbstractLet G≃Z/k1Z⊕⋯⊕Z/kNZ be a finite abelian group with ki|ki−1(2≤i≤N). For a matrix Y=(ai,j)∈ZR×...
AbstractGiven a finite abelian group G (written additively), and a subset S of G, the size r(S) of t...
This article has been retracted at the request of the Editor-in-Chief and author. Please see http://...
The Balog-Szemerédi-Gowers theorem has a rich history, and is a very useful tool in additive combin...
AbstractLet A be a set of k⩾5 elements of an Abelian group G in which the order of the smallest nonz...
Let G be a finite Abelian group and A a subset of G. The spectrum of A is the set of its large Fouri...
A subset $\mathcal{A}$ of a finite abelian group $(G,+)$ is called a $B_h$ set on $G$ if all sums of...
AbstractFor a prime p, a subset S of Zp is a sumset if S=A+A for some A⊂Zp. Let f(p) denote the maxi...
We prove the following conjecture of Shkredov and Solymosi: every subset $A \subset \mathbf{Z}^2$ su...
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