Structural additive theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2013
|
| Series: | Developments in mathematics
30 |
| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9783319004150 9783319004167 |
| DOI: | 10.1007/978-3-319-00416-7 |
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Record in the Search Index
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| adam_text | STRUCTURAL ADDITIVE THEORY
/ GRYNKIEWICZ, DAVID J.
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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 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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
STRUCTURAL ADDITIVE THEORY
/ GRYNKIEWICZ, DAVID J.
: 2013
ABSTRACT / INHALTSTEXT
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.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Grynkiewicz, David J. |
| author_facet | Grynkiewicz, David J. |
| author_role | aut |
| author_sort | Grynkiewicz, David J. |
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| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-00416-7 |
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| spelling | Grynkiewicz, David J. Verfasser aut Structural additive theory David J. Grynkiewicz Heidelberg [u.a.] Springer 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Developments in mathematics 30 Kombinatorik (DE-588)4031824-2 gnd rswk-swf Additive Zahlentheorie (DE-588)4141387-8 gnd rswk-swf Additive Zahlentheorie (DE-588)4141387-8 s Kombinatorik (DE-588)4031824-2 s 1\p DE-604 Developments in mathematics 30 (DE-604)BV036889254 30 https://doi.org/10.1007/978-3-319-00416-7 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026059734&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026059734&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Grynkiewicz, David J. Structural additive theory Developments in mathematics Kombinatorik (DE-588)4031824-2 gnd Additive Zahlentheorie (DE-588)4141387-8 gnd |
| subject_GND | (DE-588)4031824-2 (DE-588)4141387-8 |
| title | Structural additive theory |
| title_auth | Structural additive theory |
| title_exact_search | Structural additive theory |
| title_full | Structural additive theory David J. Grynkiewicz |
| title_fullStr | Structural additive theory David J. Grynkiewicz |
| title_full_unstemmed | Structural additive theory David J. Grynkiewicz |
| title_short | Structural additive theory |
| title_sort | structural additive theory |
| topic | Kombinatorik (DE-588)4031824-2 gnd Additive Zahlentheorie (DE-588)4141387-8 gnd |
| topic_facet | Kombinatorik Additive Zahlentheorie |
| url | https://doi.org/10.1007/978-3-319-00416-7 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026059734&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026059734&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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