Structural additive theory / David J. Grynkiewicz.

Includes bibliographical references and index.

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; 1
13. The DeVos-Goddyn-Mohar Theorem;
14. The partition theoroem I;
15. The partition theorem II;
16. The -weighted gao theorem;
17. Group algebras: an upper bound for the davenport constant;
18. Character and linear algebraic methods: snevily's conjecture;
19. Character sum and fourier analytic methods: r-critical pairs I;
20. Freiman homomorphisms revisited;
21. The isoperimetric method: sidon sets and r-critical pairs II;
22. The polynomial method: the Erdos-Heilbronn conjecture;

References;
Index.

This book is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail.