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Irregularities of Partitions pp 71–87Cite as

On the Distribution of Monochromatic Configurations

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Part of the book series: Algorithms and Combinatorics 8 ((AC,volume 8))

Abstract

Much of Ramsey theory is concerned with the study of structure which is preserved under finite partitions, (eg., see [8], [9], [12]). Some of the earliest results in the field were the following.

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References

  1. V. Bergelson, A density statement generalizing Schur’s theorem, J.Combin. Th. (A) 43 (1986), 338–343.

    Article  MathSciNet  MATH  Google Scholar 

  2. W. Deuber, R.L. Graham, H.J. Prőmel, B. Voigt, A Canonical Partition Theorem for Equivalence Relations on 2t, J. Combinatorial Th. (A), 34, (1983), 331–339.

    Article  MATH  Google Scholar 

  3. W. Deuber, Partitionen und lineare Gleichungsysteme, Math. Z. 133 (1973), 109–123.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Frankl, R.L. Graham and V. Rödl, Quantitative theorems for regular systems of equations, (to appear).

    Google Scholar 

  5. P. Frankl, R.L. Graham and V. Rödl, Iterated combinatorial density theorems, (to appear).

    Google Scholar 

  6. H. Furstenberg, Y. Katznelson, An ergodic Szemerédi theorem for commuting transformations, J.Analyse Math. 34 (1978), 275–291.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Furstenberg, Y. Katznelson and D. Ornstein, The ergodic theoretic proof of Szemerédi’s Theorem, Bull Amer. Math. Soc. 7 (1982), 527–552.

    Article  MathSciNet  MATH  Google Scholar 

  8. R.L. Graham, Rudiments of Ramsey Theory, Regional Conference Series in Mathematics, no. 45, AMS, 1981.

    Google Scholar 

  9. R.L. Graham, B.L. Rothschild, J.H. Spencer, Ramsey Theory, John Wiley & Sons, Inc., 1980.

    Google Scholar 

  10. R.L. Graham and V. Rödl, Numbers in Ramsey theory, in Surveys in Com-binatorica 1987 (C. Whitehead, ed) LMS Lecture Note Series 123, Cambridge, 1987, 111–113.

    Google Scholar 

  11. H. Lefmann, Kanonische Partitionssatze, Ph.D. Dissertation, Univ. of Bielefeld (1985).

    Google Scholar 

  12. J. Nešetřil, V. Rödl, Partition Theory and its Applications, Surveys in Combinatorics 1979 (B. Bollobás, ed) LMS Lecture Note Series 38, Cambridge, 1979, 96–157.

    Google Scholar 

  13. H.J. Prömel, V. Rödl, An elementary proof of the canonizing version of Gallai-Witt’s Theorem, J.Combinatorial Theory (A), 42, 2 (1986), 144–149.

    Article  MATH  Google Scholar 

  14. H.J. Prömel, B. Voigt, Canonical Partition Theorems for Parameter Sets, J. Combinatorial Theory (A), 35 (1985), 309–327.

    Article  Google Scholar 

  15. R. Rado, Studien zur Kombinatorik, Math. Z. 36 (1933), 242–280.

    Article  MathSciNet  Google Scholar 

  16. F.P. Ramsey, On a problem in formal logic, Proc. London Math. Soc. (2) 30 (1930), 264–285.

    Article  Google Scholar 

  17. I. Schur, Über die Kongruenz x m + y m = z m (mod p), Jber.Deutsch. Math. Verein. 25 (1916), 114–116.

    Google Scholar 

  18. E. Szemerédi, On Sets of Integers containing no k Elements in Arithmetic Progression, Acta Arith. 27 (1975), 199–245.

    MathSciNet  MATH  Google Scholar 

  19. B.L. van der Waerden, Beweis einer Baudetschen Vermutung, Nieuw. Arch. Wish. 15 (1927), 212–216.

    Google Scholar 

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Author information

Authors and Affiliations

  1. C.N.R.S., Paris, France

    P. Frankl

  2. AT & T Bell Laboratories, Murray Hill, New Jersey, 07974, USA

    R. L. Graham

  3. Czech. Technical University, Husova, Czechoslovakia

    V. Rödl

Authors
  1. P. Frankl
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  2. R. L. Graham
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  3. V. Rödl
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Editor information

Editors and Affiliations

  1. Department of Analysis, Eötvös Loránd University, Múzeum krt. 6–8, H-1088, Budapest VIII, Hungary

    Gábor Halász

  2. Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13–15, H-1053, Budapest V, Hungary

    Vera T. Sós

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© 1989 Springer-Verlag Berlin Heidelberg

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Frankl, P., Graham, R.L., Rödl, V. (1989). On the Distribution of Monochromatic Configurations. In: Halász, G., Sós, V.T. (eds) Irregularities of Partitions. Algorithms and Combinatorics 8, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61324-1_6

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  • DOI: https://doi.org/10.1007/978-3-642-61324-1_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50582-2

  • Online ISBN: 978-3-642-61324-1

  • eBook Packages: Springer Book Archive

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