Add to ORKGAbstract. Let A be a finite subset of an abelian group G. For every element bi of the sumset 2A = {b0, b1,..., b|2A|−1} we denote byDi = {a−a ′ : a, a ′ ∈ A; a+a ′ = bi} and ri = |{(a, a′) : a + a ′ = bi; a, a ′ ∈ A} | After an eventual reordering of 2A, we may assume that r0 ≥ r1 ≥... ≥ r|2A|−1. For every 1 ≤ s ≤ |2A | we define Rs(A) = |D0 ∪ D1 ∪... ∪ Ds−1 | and Rs(k) = max{Rs(A) : A ⊆ G, |A | = k}. Bourgain and Katz and Tao obtained an estimate of Rs(k) assuming s being of order k. In this note we find the exact value of Rs(k) in cases s = 1, s = 2 and s = 3. The case s = 3 appeared to be not simple. The structure of extremal sets led us to sets isomorphic to planar sets having a rather unexpected form of a perfect hexagon. The pr...
We survey the state of research to determine the maximum size of a nonspanning subset of a finite ab...
Abstract. Let G be a finite abelian group, and k1, k2 be two integers. For any subset A ⊂ G, let rk1...
Given a finite abelian group G (written additively), and a subset S of G, the size r(S) of the set (...
Abstract. Let G ' Z/k1Z ⊕ · · · ⊕ Z/kNZ be a finite abelian group with ki|ki−1 (2 ≤ i ≤ N)....
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×...
International audienceLet A, B and S be three subsets of a finite Abelian group G. The restricted su...
Abstract. Let r1,..., rs be non-zero integers satisfying r1 + · · ·+ rs = 0. Let G ' Z/k1Z ⊕ ...
AbstractGiven a finite abelian group G (written additively), and a subset S of G, the size r(S) of t...
A subset S = {s 1 , . . . , s k of an Abelian group G is called an S t -set of size k if all su...
Given a finite abelian group $G$ and a subset $J\subset G$ with $0\in J$, let $D_{G}(J,N)$ be the ma...
AbstractA subset S={s1,…,sk} of an Abelian group G is called an St-set of size k if all sums of t di...
Let G be a finite abelian group of order g: We determine, for all 1pr; spg; the minimal size mGðr; s...
AbstractLet G be an additive abelian group whose finite subgroups are all cyclic. Let A1,…,An(n>1) b...
AbstractWe show that for any set A in a finite Abelian group G that has at least c|A|3 solutions to ...
1. Introduction * Let X = {xl9 •••, xn} be a set of (not necessarily distinct)1 elements of a torsio...
We survey the state of research to determine the maximum size of a nonspanning subset of a finite ab...
Abstract. Let G be a finite abelian group, and k1, k2 be two integers. For any subset A ⊂ G, let rk1...
Given a finite abelian group G (written additively), and a subset S of G, the size r(S) of the set (...
Abstract. Let G ' Z/k1Z ⊕ · · · ⊕ Z/kNZ be a finite abelian group with ki|ki−1 (2 ≤ i ≤ N)....
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×...
International audienceLet A, B and S be three subsets of a finite Abelian group G. The restricted su...
Abstract. Let r1,..., rs be non-zero integers satisfying r1 + · · ·+ rs = 0. Let G ' Z/k1Z ⊕ ...
AbstractGiven a finite abelian group G (written additively), and a subset S of G, the size r(S) of t...
A subset S = {s 1 , . . . , s k of an Abelian group G is called an S t -set of size k if all su...
Given a finite abelian group $G$ and a subset $J\subset G$ with $0\in J$, let $D_{G}(J,N)$ be the ma...
AbstractA subset S={s1,…,sk} of an Abelian group G is called an St-set of size k if all sums of t di...
Let G be a finite abelian group of order g: We determine, for all 1pr; spg; the minimal size mGðr; s...
AbstractLet G be an additive abelian group whose finite subgroups are all cyclic. Let A1,…,An(n>1) b...
AbstractWe show that for any set A in a finite Abelian group G that has at least c|A|3 solutions to ...
1. Introduction * Let X = {xl9 •••, xn} be a set of (not necessarily distinct)1 elements of a torsio...
We survey the state of research to determine the maximum size of a nonspanning subset of a finite ab...
Abstract. Let G be a finite abelian group, and k1, k2 be two integers. For any subset A ⊂ G, let rk1...
Given a finite abelian group G (written additively), and a subset S of G, the size r(S) of the set (...