Additive combinatorics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2010
|
| Edition: | Paperback edition |
| Series: | Cambridge studies in advanced mathematics
105 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xviii, 512 Seiten |
| ISBN: | 9780521853866 9780521136563 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804141219364732928 |
|---|---|
| adam_text | Contents
Prologue page
xi
1
2
6
9
19
23
27
33
37
42
45
51
54
57
59
69
78
83
92
99
3 Additive
geometry
112
3.1 Additive
groups
113
3.2
Progressions
119
3.3
Convex bodies
122
vu
1
The probabilistic method
1.1
The first moment method
1.2
The second moment method
1.3
The exponential moment method
1.4
Correlation inequalities
1.5
The
Lovász
local lemma
1.6
Janson s inequality
1.7
Concentration of polynomials
1.8
Thin bases of higher order
1.9
Thin Waring bases
1.10
Appendix: the distribution of the primes
2
Sum set estimates
2.1
Sum sets
2.2
Doubling constants
2.3
Ruzsa distance and additive energy
2.4
Covering lemmas
2.5
The
Balog-Szemerédi-Gowers
theorem
2.6
Symmetry sets and unbalanced partial sum sets
2.7
Non-commutative analogs
2.8
Elementary sum-product estimates
viii Contents
3.4
The Brunn-Minkowski inequality
127
3.5
Intersecting a convex set with a lattice
130
3.6
Progressions and proper progressions
143
4
Fourier-analytic methods
149
4.1
Basic theory
150
4.2
U
theory
156
4.3
Linear bias
160
4.4
Bohr sets
165
4.5
A(p) constants, Bh[g] sets, and dissociated sets
172
4.6
The spectrum of an additive set
181
4.7
Progressions in sum sets
189
5
Inverse sum set theorems
198
5.1
Minimal size of sum sets and the e-transform
198
5.2
Sum sets in vector spaces
211
5.3
Freiman homomorphisms
220
5.4
Torsion and torsion-free inverse theorems
227
5.5
Universal ambient groups
233
5.6
Freiman s theorem in an arbitrary group
239
6
Graph-theoretic methods
246
6.1
Basic notions
247
6.2
Independent sets, sum-free subsets, and Sidon sets
248
6.3
Ramsey theory
254
6.4
Proof of the
Balog-Szemerédi-Gowers
theorem
261
6.5
Pliinnecke s theorem
267
7
The Littlewood-Offord problem
276
7.1
The combinatorial approach
277
7.2
The Fourier-analytic approach
281
7.3
The
Esséen
concentration inequality
290
7.4
Inverse Littlewood-Offord results
292
7.5
Random Bernoulli matrices
297
7.6
The quadratic Littlewood-Offord problem
304
8
Incidence geometry
308
8.1
The crossing number of a graph
308
8.2
The
Szemerédi-Trotter
theorem
311
8.3
The sum-product problem in
R
315
8.4
Cell decompositions and the distinct distances problem
319
8.5
The sum-product problem in other fields
325
Contents ix
9
Algebraic methods
329
9.1
The combinatorial
Nullstellensatz 330
9.2
Restricted sum sets
333
9.3
Snevily s conjecture
342
9.4
Finite fields
345
9.5
Davenport s problem
350
9.6
Kemnitz s conjecture
354
9.7
Stepanov s method
356
9.8
Cyclotomic fields, and the uncertainty principle
362
10
Szemerédi s
theorem for
к
= 3 369
10.1
General strategy
372
10.2
The small torsion case
378
10.3
The integer case
386
10.4
Quantitative bounds
389
10.5
An ergodic argument
398
10.6
The
Szemerédi
regularity lemma
406
10.7
Szemerédi s
argument
411
11
Szemerédi s
theorem for
k
> 3 414
11.1
Gowers uniformity norms
417
11.2
Hard obstructions to uniformity
424
11.3
Proof of Theorem
11.6 432
11.4
Soft obstructions to uniformity
440
11.5
The infinitary ergodic approach
448
11.6
The hypergraph approach
454
11.7
Arithmetic progressions in the primes
463
12
Long arithmetic progressions in sum sets
470
12.1
Introduction
470
12.2
Proof of Theorem
12.4 473
12.3
Generalizations and variants
477
12.4
Complete and
subcomplete
sequences
480
12.5
Proof of Theorem
12.17 482
12.6
Further applications
484
Bibliography
488
Index
505
|
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| discipline | Mathematik |
| edition | Paperback edition |
| format | Book |
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| isbn | 9780521853866 9780521136563 |
| language | English |
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| physical | xviii, 512 Seiten |
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| publisher | Cambridge University Press |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Tao, Terence 1975- Verfasser (DE-588)132190370 aut Additive combinatorics Terence Tan and Van H. Vu Paperback edition Cambridge Cambridge University Press 2010 xviii, 512 Seiten txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 105 Additive combinatorics Graphentheorie (DE-588)4113782-6 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s Graphentheorie (DE-588)4113782-6 s DE-604 Vu, Van H. 1970- Verfasser (DE-588)14082247X aut Cambridge studies in advanced mathematics 105 (DE-604)BV000003678 105 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019006239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tao, Terence 1975- Vu, Van H. 1970- Additive combinatorics Cambridge studies in advanced mathematics Additive combinatorics Graphentheorie (DE-588)4113782-6 gnd Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4113782-6 (DE-588)4031824-2 |
| title | Additive combinatorics |
| title_auth | Additive combinatorics |
| title_exact_search | Additive combinatorics |
| title_full | Additive combinatorics Terence Tan and Van H. Vu |
| title_fullStr | Additive combinatorics Terence Tan and Van H. Vu |
| title_full_unstemmed | Additive combinatorics Terence Tan and Van H. Vu |
| title_short | Additive combinatorics |
| title_sort | additive combinatorics |
| topic | Additive combinatorics Graphentheorie (DE-588)4113782-6 gnd Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Additive combinatorics Graphentheorie Kombinatorik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019006239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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