Behrend-type constructions for sets of linear equations

Acta Arithmetica

Volumn 122, Issue 1, 2006, Pages 17-33

  Shapira, Asaf ^a,b  

^a Tel Aviv University ^*

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745667543     PISSN: 00651036     EISSN: None     Source Type: Journal    
DOI: 10.4064/aa122-1-2     Document Type: Article

References (9)

1. F. A. Behrend, On sets of integers which contain no three terms in arithmetical progression, Proc. Nat. Acad. Sci. USA 32 (1946), 331-332.
2. H. Furstenberg, Ergodic behaviour of diagonal measures and a theorem of Szemerédi on arithmetic progressions, J. Anal. Math. 31 (1977), 204-256.
3. W. T. Gowers, A new proof of Szemerédi's theorem, Geom. Funct. Anal. 11 (2001), 465-588.
4. S. Jukna, Extremal Combinatorics With Applications in Computer Science, Springer, 2001.
5. I. Laba and M. Lacey, On sets of integers not containing long arithmetic progressions, unpublished manuscript; http://arxiv.org/abs/math.CO/0108155.
6. R. A. Rankin, Sets of integers containing not more than a given number of terms in arithmetical progression, Proc. Roy. Soc. Edinburgh Sect. A 65 (1962), 332-344.
7. I. Z. Ruzsa, Solving a linear equation in a set of integers I, Acta Arith. 65 (1993), 259-282.
8. R. Salem and D. C. Spencer, On sets of integers which contain no three terms in arithmetical progression, Proc. Nat. Acad. Sci. USA 28 (1942), 561-563.
9. E. Szemerédi, On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27 (1975), 199-245.