Structural Additive Theory

• Main Author: Grynkiewicz, David J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Heidelberg : Springer International Publishing : Imprint: Springer, 2013.
• Series: Developments in Mathematics, 30
• Subjects: Mathematics.; Algebra.; Ordered algebraic structures.; Sequences (Mathematics).; Number theory.; Number Theory.; Sequences, Series, Summability.; Order, Lattices, Ordered Algebraic Structures.

Nestled between number theory, combinatorics, algebra, and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves,...

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.