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Author:   David J. Grynkiewicz
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   Softcover reprint of the original 1st ed. 2013
Volume:   30
Dimensions:   Width: 17.80cm , Height: 2.30cm , Length: 25.40cm
Weight:   8.206kg
ISBN:  

9783319375182

ISBN 10:   3319375180
Pages:   426
Publication Date:   23 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

1. Abelian Groups and Character Sums.- 2. Introduction to Sumsets.- 3. Simple Results for Torsion-Free Abelian Groups.- 4. Basic Results for Sumsets with an Infinite Summand.- 5. The Pigeonhole and Multiplicity Bounds.- 6. Periodic Sets and Kneser's Theorem.- 7. Compression, Complements and the 3k–4 Theorem.- 8. Additive Energy.- 9. Kemperman's Critical Pair Theory.- 10. Zero-Sums, Setpartitions and Subsequence Sums.- 11. Long Zero-Sum Free Sequences over Cyclic Groups.- 12. Pollard's Theorem for General Abelian Groups.- 13. The DeVos–Goddyn–Mohar Theorem.- 14. The Partition Theorem I.- 15. The Partition Theorem II.- 16. The Ψ-Weighted Gao Theorem.- 17. Group Algebras.- 18. Character and Linear Algebraic Methods.- 19. Character Sum and Fourier Analytic Methods.- 20. Freiman Homomorphisms Revisited.- 21. The Isoperimetric Method.- 22. The Polynomial Method.- Index.

Reviews

From the book reviews: This volume is a very welcome addition to the rather small body of books published in the area of additive combinatorics so far. ... Presenting a systematic treatment of a surprisingly wide range of topics from additive combinatorics, this book is perfectly suited as a textbook for a course in additive combinatorics ... . In many cases, the material included has not appeared in book form before and can only be found in research papers. (Vsevolod F. Lev, Mathematical Reviews, April, 2014) The book contains several recently developed theories that the author puts into Additive Theory ... . The author has added some scrumptious exercises at the end of every chapter, and supplementary notes for interested readers. ... can be used as a text at the graduate level, mainly to introduce essential topics of the 'Additive Theory', and to show to students and anybody interested to do to the research in this field, what is going on and what they can do. (Mehdi Hassani, MAA Reviews, February, 2014)

From the book reviews: This volume is a very welcome addition to the rather small body of books published in the area of additive combinatorics so far. ... Presenting a systematic treatment of a surprisingly wide range of topics from additive combinatorics, this book is perfectly suited as a textbook for a course in additive combinatorics ... . In many cases, the material included has not appeared in book form before and can only be found in research papers. (Vsevolod F. Lev, Mathematical Reviews, April, 2014) The book contains several recently developed theories that the author puts into Additive Theory ... . The author has added some scrumptious exercises at the end of every chapter, and supplementary notes for interested readers. ... can be used as a text at the graduate level, mainly to introduce essential topics of the `Additive Theory', and to show to students and anybody interested to do to the research in this field, what is going on and what they can do. (Mehdi Hassani, MAA Reviews, February, 2014)

From the book reviews: This volume is a very welcome addition to the rather small body of books published in the area of additive combinatorics so far. ... Presenting a systematic treatment of a surprisingly wide range of topics from additive combinatorics, this book is perfectly suited as a textbook for a course in additive combinatorics ... . In many cases, the material included has not appeared in book form before and can only be found in research papers. (Vsevolod F. Lev, Mathematical Reviews, April, 2014) The book contains several recently developed theories that the author puts into Additive Theory ... . The author has added some scrumptious exercises at the end of every chapter, and supplementary notes for interested readers. ... can be used as a text at the graduate level, mainly to introduce essential topics of the 'Additive Theory', and to show to students and anybody interested to do to the research in this field, what is going on and what they can do. (Mehdi Hassani, MAA Reviews, February, 2014)

From the book reviews: This volume is a very welcome addition to the rather small body of books published in the area of additive combinatorics so far. ... Presenting a systematic treatment of a surprisingly wide range of topics from additive combinatorics, this book is perfectly suited as a textbook for a course in additive combinatorics ... . In many cases, the material included has not appeared in book form before and can only be found in research papers. (Vsevolod F. Lev, Mathematical Reviews, April, 2014) The book contains several recently developed theories that the author puts into Additive Theory ... . The author has added some scrumptious exercises at the end of every chapter, and supplementary notes for interested readers. ... can be used as a text at the graduate level, mainly to introduce essential topics of the `Additive Theory', and to show to students and anybody interested to do to the research in this field, what is going on and what they can do. (Mehdi Hassani, MAA Reviews, February, 2014)

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