Sets with small sumset and rectification

Bulletin of the London Mathematical Society

Volumn 38, Issue 1, 2006, Pages 43-52

  Green, Ben ^a   Ruzsa, Imre Z ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31744444234     PISSN: 00246093     EISSN: 14692120     Source Type: Journal    
DOI: 10.1112/S0024609305018102     Document Type: Article

References (15)

1. Y. BILU, 'Structure of sets with small sumset', Structure theory of set addition, ed. J.-M. Deshouillers, et al., Astérisque 258 (Soc. Math. France, 1999) 77-108.
2. Y. BILU, V. LEV and I. Z. RUZSA, 'Rectification principles in additive number theory', Discrete Comput. Geom. 19 (1998) 343-353.
3. MEI-CHU CHANG, 'A polynomial bound in Freiman's theorem', Duke Math. J. 113 (2002) 399-419.
4. n,, Combinatorica 24 (2004) no. 1, 53-68.
5. J. A. DIAS DA SILVA and Y. O. HAMIDOUNE, 'Cyclic spaces for Grassmann derivatives and additive theory', Bull. London Math. Soc. 26 (1994) 140-146.
6. P. ERDOS and H. HEILBRONN, 'On the addition of residue classes mod p', Acta Arith. 9 (1964) 149-159.
7. G. FREIMAN, Foundations of a structural theory of set addition (Amer. Math. Soc., Providence, RI, 1973).
8. B. J. GREEN and I. Z. RUZSA, 'Freiman's theorem in an arbitrary abelian group', preprint, http://www.arXiv.org/math.NT/0505198.
9. V. F. LEV, 'Distribution of points in arcs', Integers 5 (2005) #A11.
10. I. Z. RUZSA, 'On the cardinality of A + A and A - A', Combinatorics (Keszthely 1976), Coll. Math. Soc. J. Bolyai 18 (North-Holland/Bolyai Társulat, Budapest, 1978) 933-938.
11. I. Z. RUZSA, 'An application of graph theory to additive number theory', Scientia, Ser. A 3 (1989) 97-109.
12. I. Z. RUZSA, 'Arithmetical progressions and the number of sums', Periodica Math. Hung. 25 (1992) 105-111.
13. I. Z. RUZSA, 'Generalized arithmetical progressions and sumsets', Acta Math. Hung. 65 (1994) 379-388.
14. I. Z. RUZSA, 'An analog of Freiman's theorem in groups', Structure theory of set addition, Astérisque 258 (ed. J.-M. Deshouillers, et al.; Soc. Math. France, 1999) 323-326.
15. T. SCHOEN, 'Multiple set addition in ℤp', Integers 3 (2003) paper A17 (electronic).