Structural Additive Theory (Record no. 96423)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04278nam a22004815i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-319-00416-7 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20140220082838.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 130531s2013 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783319004167 |
| -- | 978-3-319-00416-7 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-319-00416-7 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA241-247.5 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBH |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT022000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.7 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Grynkiewicz, David J. |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Structural Additive Theory |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | by David J. Grynkiewicz. |
| 264 #1 - | |
| -- | Heidelberg : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2013. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XII, 426 p. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Developments in Mathematics, |
| International Standard Serial Number | 1389-2177 ; |
| Volume number/sequential designation | 30 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algebra. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Sequences (Mathematics). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Number theory. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Number Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Sequences, Series, Summability. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Order, Lattices, Ordered Algebraic Structures. |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783319004150 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Developments in Mathematics, |
| -- | 1389-2177 ; |
| Volume number/sequential designation | 30 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-319-00416-7 |
| 912 ## - | |
| -- | ZDB-2-SMA |
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