Combinatorial Number Theory and Additive Group Theory

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ISBN: 978-3-7643-8961-1 (Print) 978-3-7643-8962-8 (Online)

Table of contents (23 chapters)

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  1. Front Matter

    Pages i-xi

  2. Additive Group Theory and Non-unique Factorizations

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 3-3

      Introduction

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      Book Chapter

      Pages 5-5

      Notation

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      Book Chapter

      Pages 7-20

      Basic concepts of non-unique factorizations

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      Book Chapter

      Pages 21-33

      The Davenport constant and first precise arithmetical results

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      Book Chapter

      Pages 35-44

      The structure of sets of lengths

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      Book Chapter

      Pages 45-56

      Addition theorems and direct zero-sum problems

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      Book Chapter

      Pages 57-86

      Inverse zero-sum problems and arithmetical consequences

  3. Sumsets and Structure

    1. Front Matter

      Pages 87-87

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      Book Chapter

      Pages 89-90

      Introduction

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      Book Chapter

      Pages 91-91

      Notation

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      Book Chapter

      Pages 93-117

      Cardinality inequalities

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      Book Chapter

      Pages 119-140

      Structure of sets with few sums

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      Book Chapter

      Pages 141-165

      Location and sumsets

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      Book Chapter

      Pages 167-184

      Density

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      Book Chapter

      Pages 185-197

      Measure and topology

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      Book Chapter

      Pages 199-210

      Exercises

  4. Thematic seminars

    1. Front Matter

      Pages 211-211

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      Book Chapter

      Pages 213-231

      A survey on additive and multiplicative decompositions of sumsets and of shifted sets

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      Book Chapter

      Pages 233-239

      On the detailed structure of sets with small additive property

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      Book Chapter

      Pages 241-252

      The isoperimetric method

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      Book Chapter

      Pages 253-265

      Additive structure of difference sets

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      Book Chapter

      Pages 267-277

      The polynomial method in additive combinatorics

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