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引用次数: 9
摘要
Freiman定理是可加组合学中关于包含大量内和的整数集的近似结构的一个经典结果。因此，我们可以推导出实数集合的一个估计:如果a∧R和∣∣12 (a + a)∣∣−| a | | a |，则a靠近它的凸包。本文在2维和3维上证明了类似结果的一个尖锐形式。
A sharp Freiman type estimate for semisums in two and three dimensional Euclidean spaces
Freiman's Theorem is a classical result in additive combinatorics concerning the approximate structure of sets of integers that contain a high proportion of their internal sums. As a consequence, one can deduce an estimate for sets of real numbers: If A ⊂ R and ∣∣ 1 2 (A+A) ∣∣− |A| |A|, then A is close to its convex hull. In this paper we prove a sharp form of the analogous result in dimensions 2 and 3.
期刊介绍：
The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics.
Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition.
The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.
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