Additive Number Theory: Inverse Problems and the Geometry of Sumsets Hardcover - 1996 - 1996th Edition
by Melvyn B. Nathanson
From the rear cover
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.
Details
- Title Additive Number Theory: Inverse Problems and the Geometry of Sumsets
- Author Melvyn B. Nathanson
- Binding Hardcover
- Edition number 1996th
- Edition 1996
- Pages 295
- Volumes 1
- Language ENG
- Publisher Springer, New York
- Date 1996-08-22
- ISBN 9780387946559 / 0387946551
- Weight 1.42 lbs (0.64 kg)
- Dimensions 9.51 x 6.29 x 0.77 in (24.16 x 15.98 x 1.96 cm)
- Library of Congress subjects Number theory
- Library of Congress Catalog Number 96012929
- Dewey Decimal Code 512.73
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Additive Number Theory: Inverse Problems and the Geometry of Sumsets (Graduate Texts in Mathematics) (Vol 165)
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Additive Number Theory: Inverse Problems and the Geometry of Sumsets (Graduate Texts in Mathematics, 165)
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