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Hans Jürgen Prömel
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Hans Jürgen Prömel: Technische Universität Darmstadt

Chapter Chapter 3 in Ramsey Theory for Discrete Structures, 2013, pp 33-39 from Springer

Abstract: 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).

Keywords: Affine Vector Space; Combinatorial Abstraction; Ramsey's Theorem; Low-dimensional Cases; Geometric Analogue (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-01315-2_3

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DOI: 10.1007/978-3-319-01315-2_3

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