A robust version of Freiman's 3 k –4 Theorem and applications
Abstract We prove a robust version of Freiman's 3 k – 4 theorem on the restricted sumset A + Γ B , which applies when the doubling constant is at most (3+ $\sqrt{5}$ )/2 in general and at most 3 in the special case when A = − B . As applications, we derive robust results with other types of ass...
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| Published in | Mathematical proceedings of the Cambridge Philosophical Society Vol. 166; no. 3; pp. 567 - 581 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
01.05.2019
|
| Online Access | Get full text |
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| Summary: | Abstract
We prove a robust version of Freiman's 3
k
– 4 theorem on the restricted sumset
A
+
Γ
B
, which applies when the doubling constant is at most (3+
$\sqrt{5}$
)/2 in general and at most 3 in the special case when
A
= −
B
. As applications, we derive robust results with other types of assumptions on popular sums, and structure theorems for sets satisfying almost equalities in discrete and continuous versions of the Riesz–Sobolev inequality. |
|---|---|
| ISSN: | 0305-0041 1469-8064 |
| DOI: | 10.1017/S0305004118000129 |