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Hales-Jewett Theorem


Geometry

Geometric Hales-Jewett Theorem ★★

Author(s): Por; Wood

Conjecture   For all integers $ k\geq1 $ and $ \ell\geq3 $, there is an integer $ f(k,\ell) $ such that for every set $ P $ of at least $ f(k,\ell) $ points in the plane, if each point in $ P $ is assigned one of $ k $ colours, then:
    \item $ P $ contains $ \ell $ collinear points, or \item $ P $ contains a monochromatic line (that is, a maximal set of collinear points receiving the same colour)

Keywords: Hales-Jewett Theorem; ramsey theory

Posted by David Wood
updated March 26th, 2014
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