عنوان

Structural Additive Theor

شابک

9783319004167

کد کشور

IR

شماره

EN-52386

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

کشور محل نشر

IR

عنوان اصلي

Structural Additive Theor

نام عام مواد

[Book]

ساير اطلاعات عنواني

:[delta

نام نخستين پديدآور

/ by David J. Grynkiewicz

محل نشرو پخش و غیره

Heidelberg

نام ناشر، پخش کننده و غيره

: Springer International Publishing :Imprint: Springer,

تاریخ نشرو بخش و غیره

, 2013.

نام خاص و کميت اثر

XII, 426 p., online resource.

عنوان فروست

(Developments in Mathematics,1389-2177

مشخصه جلد

; 30)

متن يادداشت

Electronic

متن يادداشت

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, but rather the additive structure of subsets and subsequences of an abelian group, i.e. sumsets and subsequence sums. This text 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, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune's Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.

متن يادداشت

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 Sequencesover 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 [psi]-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.?╗╣

عنوان

Developments in Mathematics,1389-2177

شماره جلد

30

موضوع مستند نشده

Mathematics

موضوع مستند نشده

Algebra

موضوع مستند نشده

Sequences (Mathematics)

موضوع مستند نشده

Number theory

موضوع مستند نشده

Electronic books

شماره رده

مستند نام اشخاص تاييد نشده

Grynkiewicz, David J.

مستند نام اشخاص تاييد نشده

SpringerLink (Online service)

کشور

ایران

نام ميزبان

9783319004150.pdf

شماره دسترسي

عادی

اطلاعات مختصر

عادی

تاريخ و ساعت مذاکره و دسترسي

9783319004150.pdf

نوع فرمت الکترونيکي

متن

وضعیت فهرست نویسی

old catalog

فرمت انتشار

e

نوع ماده

BL

پیشوند ISBD اعمال شده است

1

سطح دسترسي

a

تكميل شده

Y