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A Note on Intervals in the Hales-Jewett Theorem

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 نشر من قبل Imre Leader
 تاريخ النشر 2018
  مجال البحث
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The Hales-Jewett theorem for alphabet of size 3 states that whenever the Hales-Jewett cube [3]^n is r-coloured there is a monochromatic line (for n large). Conlon and Kamcev conjectured that, for any n, there is a 2-colouring of [3]^n for which there is no monochromatic line whose active coordinate set is an interval. In this note we disprove this conjecture.



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