A Szemerédi-type regularity lemma in abelian groups, with applications

Geometric and Functional Analysis

Volumn 15, Issue 2, 2005, Pages 340-376

  Green, Ben ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

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[No Author keywords available]

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EID: 23744478411     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-005-0509-8     Document Type: Article

References (27)

1. [A] N. ALON, Testing subgraphs in large graphs, Random Structures and Algorithms (Poznan, 2001). Random Structures Algorithms 21:3-4 (2002), 359-370.
2. [AS] N. ALON, J. SPENCER, The Probabilistic Method, 2nd Ed., Wiley 2000.
3. [B] F.A. BEHREND, On sets of integers which contain no three elements in arithmetic progression, Proc. Nat. Acad. Sci. 23 (1946), 331-332.
4. [BeHK] V. BERGELSON, B. HOST, B. KRA, Multiple recurrence and nilsequences, with an appendix by I.Z. RUZSA, preprint.
5. [Bo] B. BOLLOBÁS, Modern Graph Theory, Graduate Texts in Mathematics 184, Springer-Verlag, New York 1998.
6. [Bou] J. BOURGAIN, On triples in arithmetic progression, GAFA, Geom. funct. anal. 9:5 (1999), 968-984.
7. n, J. Combin. Theory Ser. A 61:1 (1992), 64-86.
8. [FGR] P. FRANKL, R.L. GRAHAM, V. RÖDL, On subsets of abelian groups with no 3-term arithmetic progression, J. Combin. Theory Ser. A 45:1 (1987), 157-161.
9. [FR] P. FRANKL, V. RÖDL, Extremal problems on set systems, Random Structures Algorithms 20:2 (2002), 131-164.
10. [G1] W.T. GOWERS, Lower bounds of tower type for Szemerédi's uniformity lemma, GAFA, Geom. funct. anal. 7:2 (1997), 322-337.
11. [G2] W.T. GOWERS, A new proof of Szemerédi's theorem for progressions of length four, GAFA, Geom. funct. anal. 8:3 (1998), 529-551.
12. [Gr1] B.J. GREEN, Spectral structure of sets of integers, Fourier Analysis and Convexity, Appl. Numer. Harmon. Anal., Birkhäuser (2004), 83-96.
13. [Gr2] B.J. GREEN, The Cameron-Erdös conjecture, Bull. London Math. Soc. 36:6 (2004), 769-778.
14. [Gr3] B.J. GREEN, Finite field models in additive combinatorics, Surveys in Combinatorics 2005, to appear.
15. [GrR1] B.J. GREEN, I.Z. RUZSA, Counting sumsets and sum-free sets modulo a prime, Studia Sci. Math. Hungar. 41:3 (2004), 285-293.
16. [GrR2] B.J. GREEN, I.Z. RUZSA, Counting sum-free sets in abelian groups, Israel J. Math., to appear.
17. [KS] J. KOMLÓS, M. SIMONOVITS, Szemerédi's regularity lemma and its applications in graph theory, Combinatorics, Paul Erdös is eighty 2 (Keszthely, 1993),
18. Bolyai Soc. Math. Stud. 2, János Bolyai Math. Soc., Budapest (1996), 295-352.
19. [M] R. MESHULAM, On subsets of finite abelian groups with no 3-term arithmetic progressions, J. Combin. Theory Ser. A 71:1 (1995), 168-172.
20. [PRR] Y. PENG, V. RÖDL, A. RUCINSKI, Holes in Graphs, Electron. J. Combin. 9:1 (2002).
21. [R] K.F. ROTH, On certain sets of integers, J. London Math. Soc. 28 (1953), 104-109.
22. [Ru1] I.Z. RUZSA, Solving a linear equation in a set of integers I, Acta. Arith. 65:3 (1993), 259-282.
23. [Ru2] I.Z. RUZSA, An analog of Freiman's theorem in groups, Structure theory of set addition. Astérisque 258:xv (1999), 323-326.
24. [RuSz] I.Z. RUZSA, E. SZEMERÉDI, Triple systems with no six points carrying three triangles, Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II,
25. North-Holland, Amsterdam-New York. Colloq. Math. Soc. János Bolyai 18 (1978), 939-945,
26. [Sz] E. SZEMERÉDI, Regular partitions of graphs, Problèmes combinatoires et théorie des graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976), Colloq. Internat. CNRS, 260, CNRS, Paris (1978), 399-401.
27. [T] T.C. TAO, Lecture notes 5 from Math 254A, available at http://www.math.ucla.edu/~tao/254a.1.03w/notes5.dvi