Structural Additive Theory

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,...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Grynkiewicz, David J. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2013.
Edición:1st ed. 2013.
Colección:Developments in Mathematics, 30
Temas:
Number theory.
Sequences (Mathematics).
Algebra.
Number Theory.
Sequences, Series, Summability.
Order, Lattices, Ordered Algebraic Structures.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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