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Definitions and Basic Examples

In: Ramsey Theory for Discrete Structures

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  • Hans Jürgen Prömel

    (Technische Universität Darmstadt)

Abstract

In their by now classical paper Ramsey’s theorem for n-parameter sets Graham and Rothschild (1971) introduced the concept of parameter sets. The idea was to find a combinatorial abstraction of linear and affine vector spaces over finite fields. This was motivated by a conjecture of Rota, proposing a geometric analogue to Ramsey’s theorem. In fact, the Ramsey theorem for n-parameter sets implies Rota’s conjecture directly for lower dimensional cases and, as it has turned out, the method used in the proof of this theorem contains also the seeds of the ideas to prove Rota’s conjecture in its full strength. This was done in Graham, Leeb and Rothschild (1972).

Suggested Citation

  • Hans Jürgen Prömel, 2013. "Definitions and Basic Examples," Springer Books, in: Ramsey Theory for Discrete Structures, edition 127, chapter 0, pages 33-39, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-01315-2_3
    DOI: 10.1007/978-3-319-01315-2_3
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