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Volumn 184, Issue 1, 2011, Pages 93-128

An improved construction of progression-free sets

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EID: 79960987955     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/s11856-011-0061-1     Document Type: Article
Times cited : (70)

References (34)
  • 1
    • 77951687705 scopus 로고
    • On a conjecture of Erdo{double acute}s and Straus on non-averaging sets of integers
    • Winnipeg, Man.: Utilitas Mathematica
    • H. L. Abbott, On a conjecture of Erdo{double acute}s and Straus on non-averaging sets of integers, in Proceedings of the 5th British Combinatorial Conference, Congress Numerartium XV, Utilitas Mathematica, Winnipeg, Man., 1975, pp. 1-4.
    • (1975) Proceedings of the 5th British Combinatorial Conference, Congress Numerartium XV , pp. 1-4
    • Abbott, H.L.1
  • 2
    • 84972529983 scopus 로고
    • Extremal problems on non-averaging and non-dividing sets
    • H. L. Abbott, Extremal problems on non-averaging and non-dividing sets, Pacific Journal of Mathematics 91 (1980), 1-12.
    • (1980) Pacific Journal of Mathematics , vol.91 , pp. 1-12
    • Abbott, H.L.1
  • 3
    • 0042283427 scopus 로고
    • On the Erdo{double acute}s-Straus non-averaging set problem
    • H. L. Abbott, On the Erdo{double acute}s-Straus non-averaging set problem, Acta Mathematica Hungarica 47 (1986), 117-119.
    • (1986) Acta Mathematica Hungarica , vol.47 , pp. 117-119
    • Abbott, H.L.1
  • 5
    • 0001432978 scopus 로고
    • A lower bound for the volumes of strictly convex bodies with many boundary points
    • G. E. Andrews, A lower bound for the volumes of strictly convex bodies with many boundary points, Transactions of the American Mathematical Society 106 (1963), 270-279.
    • (1963) Transactions of the American Mathematical Society , vol.106 , pp. 270-279
    • Andrews, G.E.1
  • 6
    • 0008979454 scopus 로고
    • Statistics of integer convex polytopes
    • V. I. Arnold, Statistics of integer convex polytopes (in Russian), Funk. Anal. Pril. 14 (1980), no. 1, 1-3.
    • (1980) Funk. Anal. Pril. , vol.14 , Issue.1 , pp. 1-3
    • Arnold, V.I.1
  • 8
    • 0039984348 scopus 로고    scopus 로고
    • The convex hull of the integer points in a large ball
    • I. Barany and D. G. Larman, The convex hull of the integer points in a large ball, Mathematische Annalen 312 (1998), 167-181.
    • (1998) Mathematische Annalen , vol.312 , pp. 167-181
    • Barany, I.1    Larman, D.G.2
  • 9
    • 0001587222 scopus 로고
    • On sets of integers which contain no three terms in arithmetic progression
    • F. Behrend, On sets of integers which contain no three terms in arithmetic progression, Proceedings of the National Academy of Sciences U. S. A 32 (1946), 331-332.
    • (1946) Proceedings of the National Academy of Sciences U.S.A , vol.32 , pp. 331-332
    • Behrend, F.1
  • 10
    • 0043285699 scopus 로고
    • On the lower estimation of non-averaging sets
    • A. P. Bosznay, On the lower estimation of non-averaging sets, Acta Mathematica Hungarica 53 (1989), 155-157.
    • (1989) Acta Mathematica Hungarica , vol.53 , pp. 155-157
    • Bosznay, A.P.1
  • 12
    • 58449129683 scopus 로고    scopus 로고
    • Roth's theorem in progressions revisited
    • J. Bourgain, Roth's theorem in progressions revisited, Journal D'Analise Mathematique 104 (2008), 155-192.
    • (2008) Journal D'analise Mathematique , vol.104 , pp. 155-192
    • Bourgain, J.1
  • 14
    • 77951671627 scopus 로고    scopus 로고
    • An improved construction of progression-free sets
    • Austin, TX, USA
    • M. Elkin, An improved construction of progression-free sets, in ACM-SIAM Symposium on Discrete Algorithms, SODA'10, Austin, TX, USA, 2010, pp. 886-905.
    • (2010) ACM-SIAM Symposium on Discrete Algorithms, SODA'10 , pp. 886-905
    • Elkin, M.1
  • 19
    • 76249111541 scopus 로고    scopus 로고
    • New bounds for Szemerédi's theorem, II: A new bound for r4(n)
    • (W. W. L. Chen, W. T. Gowers, H. Halber Stam, W. M. Schmidt, R. C. Vaughan eds.)
    • B. Green and T. Tao, New bounds for Szemerédi's theorem, II: A new bound for r4(n), in Analytic Number Theory: essays in honour of Klaus Roth, (W. W. L. Chen, W. T. Gowers, H. Halber Stam, W. M. Schmidt, R. C. Vaughan eds.) 2009, pp. 180-204.
    • (2009) Analytic Number Theory: Essays in honour of Klaus Roth , pp. 180-204
    • Green, B.1    Tao, T.2
  • 20
    • 79960986805 scopus 로고    scopus 로고
    • A note on Elkin's improvement of Behrend's construction
    • B. Green and J. Wolf, A note on Elkin's improvement of Behrend's construction, Additive Number Theory (2010), 141-144.
    • (2010) Additive Number Theory , pp. 141-144
    • Green, B.1    Wolf, J.2
  • 21
  • 22
    • 0000942593 scopus 로고
    • Über Gitterpunkte und konvex Kurven
    • V. Jarnik, Über Gitterpunkte und konvex Kurven, Mathematische Zeitschrift 2 (1925), 500-518.
    • (1925) Mathematische Zeitschrift , vol.2 , pp. 500-518
    • Jarnik, V.1
  • 25
    • 33746622494 scopus 로고
    • On non-averaging sets of integers
    • L. Moser, On non-averaging sets of integers, Canadian Journal of Mathematics 5 (1953), 245-253.
    • (1953) Canadian Journal of Mathematics , vol.5 , pp. 245-253
    • Moser, L.1
  • 27
    • 84973957311 scopus 로고
    • Sets not containing more than a given number of terms in arithmetic progression
    • R. A. Rankin, Sets not containing more than a given number of terms in arithmetic progression, Proceedings of the Royal Society of Edinburgh. Section A 65 (1960), 332-344.
    • (1960) Proceedings of the Royal Society of Edinburgh. Section A , vol.65 , pp. 332-344
    • Rankin, R.A.1
  • 29
    • 0002077527 scopus 로고
    • Solving a linear equation on a set of integers I
    • I. Z. Ruzsa, Solving a linear equation on a set of integers I, Acta Arithmetica 65 (1993), 259-282.
    • (1993) Acta Arithmetica , vol.65 , pp. 259-282
    • Ruzsa, I.Z.1
  • 31
    • 33745667543 scopus 로고    scopus 로고
    • Behrend-type constructions for sets of linear equations
    • A. Shapira, Behrend-type constructions for sets of linear equations, Acta Arithmetica 122 (2006), 17-33.
    • (2006) Acta Arithmetica , vol.122 , pp. 17-33
    • Shapira, A.1
  • 32
    • 0002097616 scopus 로고
    • Über die Klassenzahl quadratischer Zahlkörper
    • C. L. Siegel, Über die Klassenzahl quadratischer Zahlkörper, Acta Arithmetica 1 (1935), 83-86.
    • (1935) Acta Arithmetica , vol.1 , pp. 83-86
    • Siegel, C.L.1
  • 33
    • 0001549458 scopus 로고
    • On sets of integers containing no κ elements in arithmetic progression
    • E. Szemerédi, On sets of integers containing no κ elements in arithmetic progression, Acta Arithmetica 27 (1975), 299-345.
    • (1975) Acta Arithmetica , vol.27 , pp. 299-345
    • Szemerédi, E.1
  • 34
    • 0000590051 scopus 로고
    • Beweis einer Baudetischen Vermutung
    • B. L. van der Waerden, Beweis einer Baudetischen Vermutung, Nieuw Archief voor Wiskunde 2(15) (1927), 212-216.
    • (1927) Nieuw Archief Voor Wiskunde , vol.2 , Issue.15 , pp. 212-216
    • van der Waerden, B.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.