A Note on Intervals in the Hales-Jewett Theorem

2018/02/09 by Leader, Imre, Raty, Eero · 1 citation
#05D10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.03087

Abstract

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.

Cited by

• Lower Bounds for the Hales-Jewett Numbers via Symmetric and One-Weight Colorings

Related

• Another Note on Intervals in the Hales-Jewett Theorem
• Intervals in the Hales-Jewett theorem
• Colouring versus density in integers and Hales-Jewett cubes
• An upper bound for the Hales-Jewett number HJ(4,2)
• A new proof of the density Hales-Jewett theorem