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- Title
SETS WITH SEVERAL CENTERS OF SYMMETRY.
- Authors
FREIMAN, GREGORY A.; STANCHESCU, YONUTZ V.
- Abstract
Let A be a finite subset of the group ℤ2. Let C = {c0, c1,...,cs-1} be a finite set of s distinct points in the plane. For every 0 ≤ i ≤ s -1, we define Di = {a - a′ : a ∈ A, a′ ∈ A, a + a′ = 2ci} and Rs(A) = |D0 ∪ D1 ∪...∪ Ds-1|. In [1, 2], we found the maximal value of Rs(A) in cases s = 1, s = 2 and s = 3 and studied the structure of A assuming that R3(A) is equal or close to its maximal value. In this paper, we examine the case of s = 4 centers of symmetry and we find the maximal value of R4(A). Moreover, in cases when the maximal value is attained, we will describe the structure of extremal sets.
- Subjects
SET theory; MATHEMATICAL symmetry; ADDITIVE combinatorics; GROUP theory; FINITE element method; MATHEMATICAL analysis
- Publication
International Journal of Number Theory, 2011, Vol 7, Issue 5, p1115
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042111004174