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Intervals in the Hales-Jewett theorem. -Eero Raty (dpmms).

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The Hales-Jewett theorem for alphabet of size 3 states that whenever the cube {1, 2, 3}n is r-coloured there exists a monochromatic line for n large. Given a line l, the set of active coordinates of l is the set of those coordinates that are allowed to vary. In this talk I will consider the following question: given r, what is the smallest number t so that for any r-colouring of [3]n (n large) there exists a monochromatic line whose active set of coordinates is an union of at most t intervals.

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