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Introduction Ramsey Theory Old and New

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Mathematics of Ramsey Theory

Part of the book series: Algorithms and Combinatorics ((AC,volume 5))

Abstract

The purpose of this introduction is to outline scope and intentions of this volume. We also state some classical results. This historical perspective will be of some use to a (non-specialist) reader.

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References

  • Abramson, F., Harrington, L.A. (1978): Models without indiscernibles. J. Symb. Logic 43, 572–600

    Article  MathSciNet  MATH  Google Scholar 

  • Alon, N., Maass, W. (1986): Ramsey theory and lower bounds for branching programs. Proc. 27th IEEE FOCS, pp. 410–417

    Google Scholar 

  • Baumgartner, J.E., Taylor, A.D. (1978): Partition theorems and ultrafilters. Trans. Am. Math. Soc. 241, 283–309

    Article  MathSciNet  MATH  Google Scholar 

  • Burkill, H., Mirsky, L. (1973): Monotonicity. J. Math. Anal. Appl. 41, 391–410

    Article  MathSciNet  MATH  Google Scholar 

  • Chvátal, V. (1971): Hypergraphs and Ramseyan theorems. Proc. Am. Math. Soc. 27, 434–440

    Article  MATH  Google Scholar 

  • Deuber, W. (1973): Partitionen und lineare Gleichungssysteme. Math. Z. 133, 109–123

    Article  MathSciNet  MATH  Google Scholar 

  • Erdös, P., Rado, R. (1952): Combinatorial theorems on classifications of subsets of a given set. Proc. Lond. Math. Soc., III. Ser. 2, 417–439

    Article  MATH  Google Scholar 

  • Erdös, P., Szekeres, G. (1935): A combinatorial problem in geometry. Compos. Math. 2, 463–470

    MATH  Google Scholar 

  • Erdös, P., Hajnal, A., Rado, R. (1965): Partition relations for cardinal numbers. Acta. Math. Acad. Sci. Hung. 16, 93–196

    Article  MATH  Google Scholar 

  • Erdös, P., Hajnal, A., Maté, A., Rado, R. (1984): Combinatorial set theory: partition relations for cardinals. North Holland, Amsterdam (Stud. Logic Found. Math., Vol. 106)

    MATH  Google Scholar 

  • Fürstenberg, H. (1977): Ergodic behaviour of diagonal measures and a theorem of Szemeredi on arithmetic progressions. J. Anal. Math. 31, 204–256

    Article  Google Scholar 

  • Fürstenberg, H. (1981): Recurrence in ergodic theory and combinatorial number theory. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Fürstenberg, H. (1981): Poincaré recurrence and number theory. Bull. Am. Math. Soc., New Ser. 5, 211–234

    Article  MATH  Google Scholar 

  • Graham, R.L. (1984): Recent developments in Ramsey theory. In: Ciesielski, Z., Olech, C. (eds.): Proc. International Congress of Mathematicians (Warsaw, 1983), Vol. 2. North Holland, Amsterdam, pp. 1555–1569

    Google Scholar 

  • Graham, R.L., Rödl, V. (1987): Numbers in Ramsey theory. In: Whitehead, C. (ed.): Surveys in combinatorics 1987. Cambridge University Press, Cambridge, pp. 111–153 (Lond. Math. Soc. Lect. Note Ser., Vol. 123)

    Google Scholar 

  • Graham, R.L., Rothschild, B. (1971): Ramsey’s theorem for n-parameter sets. Trans. Am. Math. Soc. 159, 257–292

    MathSciNet  MATH  Google Scholar 

  • Graham, R.L., Leeb, K., Rothschild, B. (1972): Ramsey’s theorem for a class of categories. Adv. Math. 8, 417–433

    Article  MathSciNet  MATH  Google Scholar 

  • Graham, R.L., Rothschild, B., Spencer, J. (1980): Ramsey theory. J. Wiley & Sons, New York, NY

    MATH  Google Scholar 

  • Hales, A.W., Jewett, R.I. (1963): Regularity and positional games. Trans. Am. Math. Soc. 106, 222–229

    Article  MathSciNet  MATH  Google Scholar 

  • Hilbert, D. (1892): Uber die Irreduzibilität ganzer rationaler Funktionen mit ganzzahligen Koeffizienten. J. Reine Angew. Math. 110, 104–129

    Article  Google Scholar 

  • Leeb, K. (1973): Vorlesungen über Pascaltheorie. Universität Erlangen-Nürnberg (Unpublished)

    Google Scholar 

  • Moran, S., Snir, M., Manber, U. (1985): Applications of Ramsey’s theorem to decision tree complexity. J. Assoc. Comput. Mach. 32, 938–949

    Article  MathSciNet  MATH  Google Scholar 

  • Nash-Williams, C.St.J.A. (1965): On well-quasi-ordering infinite sequences. Proc. Camb. Philos. Soc. 61, 697–720

    Article  MathSciNet  MATH  Google Scholar 

  • Nešetřil, J. (1984): Some nonstandard Ramsey-like applications. Theor. Comput. Sci. 34, 3–15

    Article  MATH  Google Scholar 

  • Nešetřil, J., Rödl, V. (1975): Type theory of partition properties of graphs. In: Recent advances in graph theory, Academia, Praha, pp. 405–412

    Google Scholar 

  • Nešetřil, J., Rödl, V. (1979): Partition theory and its application. In: Bollobás, B. (Ed.): Surveys in combinatorics. Cambridge University Press, Cambridge, pp. 96–156 (Lond. Math. Soc. Lect. Note Ser., Vol. 38)

    Google Scholar 

  • Nešetřil, J., Rödl, V. (1985): Two remarks on Ramsey’s theorem. Discrete Math. 54, 339–341

    Article  MathSciNet  MATH  Google Scholar 

  • Nešetřil, J., Rödl, V. (1987): Strong Ramsey theorems for Steiner systems. Trans. Am. Math. Soc. 303, 183–192

    MATH  Google Scholar 

  • Nešetřil, J., Thomas, R. (1987): Well quasi-orderings, long games and a combinatorial study of undecidability. In: Simpson, S.G. (ed.): Logic and combinatorics. American Mathematical Society, Providence, RI, pp. 281–293 (Contemp. Math., Vol. 65)

    Google Scholar 

  • Paris, J.B., Harrington, L.A. (1977): A mathematical incompleteness in Peano arithmetic. In: Barwise, J. (ed.): Handbook of mathematical logic. North Holland, Amsterdam, pp. 1133–1142 (Stud. Logic Found. Math., Vol. 90)

    Chapter  Google Scholar 

  • Ramsey, F.P. (1930): On a problem of formal logic. Proc. Lond. Math. Soc., II. Ser. 30, 264–286

    Article  Google Scholar 

  • Schur, I. (1916): Über die Kongruenz a?m+i/m=zm (mod p). J. Deutsche Math. Verein. 25, 114–116

    MATH  Google Scholar 

  • Vilfan, B. (1976): Lower bounds for the size of expressions for certain functions in d-ary logic. Theor. Comput. Sci. 2, 249–269

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  • Yao, A.C. (1981): Should tables be sorted? J. Assoc. Comput. Mach. 28, 615–628

    Article  MathSciNet  MATH  Google Scholar 

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Nešetřil, J., Rödl, V. (1990). Introduction Ramsey Theory Old and New. In: Nešetřil, J., Rödl, V. (eds) Mathematics of Ramsey Theory. Algorithms and Combinatorics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72905-8_1

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  • DOI: https://doi.org/10.1007/978-3-642-72905-8_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-72907-2

  • Online ISBN: 978-3-642-72905-8

  • eBook Packages: Springer Book Archive

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