Structural Additive Theory

1. Abelian Groups and Character Sums
David J. Grynkiewicz

Part I. Sumsets

2. Introduction to Sumsets
David J. Grynkiewicz

3. Simple Results for Torsion-Free Abelian Groups
David J. Grynkiewicz

4. Basic Results for Sumsets with an Infinite Summand
David J. Grynkiewicz

5. The Pigeonhole and Multiplicity Bounds
David J. Grynkiewicz

6. Periodic Sets and Kneser’s Theorem
David J. Grynkiewicz

7. Compression, Complements and the 3k−4 Theorem
David J. Grynkiewicz

8. Additive Energy
David J. Grynkiewicz

9. Kemperman’s Critical Pair Theory
David J. Grynkiewicz

Part II. Subsequence Sums

10. Zero-Sums, Setpartitions and Subsequence Sums
David J. Grynkiewicz

11. Long Zero-Sum Free Sequences over Cyclic Groups
David J. Grynkiewicz

12. Pollard’s Theorem for General Abelian Groups
David J. Grynkiewicz

13. The DeVos-Goddyn-Mohar Theorem
David J. Grynkiewicz

14. The Partition Theorem I
David J. Grynkiewicz

15. The Partition Theorem II
David J. Grynkiewicz

16. The Ψ-Weighted Gao Theorem
David J. Grynkiewicz

Part III. Advanced Methods

17. Group Algebras: An Upper Bound for the Davenport Constant
David J. Grynkiewicz

18. Character and Linear Algebraic Methods: Snevily’s Conjecture
David J. Grynkiewicz

19. Character Sum and Fourier Analytic Methods: r-Critical Pairs I
David J. Grynkiewicz

20. Freiman Homomorphisms Revisited
David J. Grynkiewicz

21. The Isoperimetric Method: Sidon Sets and r-Critical Pairs II
David J. Grynkiewicz

22. The Polynomial Method: The Erdős-Heilbronn Conjecture
David J. Grynkiewicz

Keywords: Mathematics, Number Theory, Sequences, Series, Summability, Order, Lattices, Ordered Algebraic Structures