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).
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Prömel, H.J. (2013). Definitions and Basic Examples. In: Ramsey Theory for Discrete Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-01315-2_3
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DOI: https://doi.org/10.1007/978-3-319-01315-2_3
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