Additive Number Theory: Inverse Problems and the Geometry of Sumsets
Additive Number Theory: Inverse Problems and the Geometry of Sumsets
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DOI：
10.5860/choice.35-0343a
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发表时间：
1996-08
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影响因子：
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通讯作者：
M. Nathanson
中科院分区：
文献类型：
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作者：
M. Nathanson
许多古典添加剂数论问题的直接问题,一开始设置一个自然数和整数H - > 2,并试图描述sumset公顷的结构组成的所有的H元素的a。相比之下,在一个反问题,始于一个sumset哈,并试图描述底层的结构设置a .近年来已经有ramrkable逆问题的研究进展为有限集的整数。特别地，有一些重要而美丽的逆定理是由Freiman， Kneser, Plunnecke， Vosper等人提出的。本卷包括他们的结果，并以Ruzsa对Freiman的深度定理的一个优雅的证明为高潮，该定理证明了具有小集合的有限整数集必须是n维等差数列的一个大子集。
Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plunnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.