Additive Number Theory: Inverse Problems and the Geometry of Sumsets by Melvyn B. Nathanson

Additive Number Theory: Inverse Problems and the Geometry of Sumsets

byMelvyn B. Nathanson

Hardcover | August 22, 1996

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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, Plünnecke, 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.

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Title:Additive Number Theory: Inverse Problems and the Geometry of SumsetsFormat:HardcoverDimensions:310 pages, 9.21 × 6.14 × 0.27 inPublished:August 22, 1996Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:0387946551

ISBN - 13:9780387946559

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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(actual symbol not reproducible)2 and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. In 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 remarkable 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, Vospel and others. This volume includes their results and culminates with an elegant proof by Rusza 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. Inverse problems are a central topic in additive number theory. This graduate text gives a comprehensive and self-contained account of this subject. In particular, it contains complete proofs of results from exterior alg