David J. Grynkiewicz

Structural additive theory

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 Knesers Theorem.- 7. Compression, Complements and the 3k-4 Theorem.- 8. Additive Energy.- 9. Kempermans Critical Pair Theory.- 10. Zero-Sums, Setpartitions and Subsequence Sums.- 11. Long Zero-Sum Free Sequences over Cyclic Groups.- 12. Pollards Theorem for General Abelian Groups.- 13. The DeVos-Goddyn-Mohar Theorem.- 14. The Partition Theorem I.- 15. The Partition Theorem II.- 16. The ?-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.

Inverse zero-sum problems {III}

Let

A Step Beyond Kemperman's Structure Theorem

G

Quasi-periodic decompositions and the Kemperman structure theorem

be a finite abeilian group. A sequence

On four colored sets with nondecreasing diameter and the Erdös-Ginzburg-Ziv theorem

S

A weighted generalization of two theorems of Gao

with terms from

Products of two atoms in Krull monoids and arithmetical characterizations of class groups

G

The Connectivity of addition Cayley graphs

is zero-sum if the sum of terms in

A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems

S

Note on a conjecture of Graham

equals zero. It is a minimal zero-sum sequence if no proper, nontrivial subsequence is zero-sum. The maximal length of a minimal zero-sum subsequence in