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Additive Number Theory: Inverse Problems and the Geometry of Sumsets: 165 (Graduate Texts in Mathematics, 165) - Tapa dura

Nathanson, Melvyn B.

 
9780387946559: Additive Number Theory: Inverse Problems and the Geometry of Sumsets: 165 (Graduate Texts in Mathematics, 165)
Tapa dura
ISBN 10: 0387946551 ISBN 13: 9780387946559
Editorial: Springer, 1996

Sinopsis

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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De la contraportada

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 algebra, combinatorics, graph theory, and the geometry of numbers that are used in the proofs of the principal inverse theorems. The only prerequisites for the book are undergraduate courses in algebra, number theory, and analysis.

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Editorial
Springer
Año de publicación
1996
Idioma
Inglés
ISBN 10 
0387946551
ISBN 13 
9780387946559
Encuadernación
Tapa dura
Número de páginas
316
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

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