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arxiv: 1802.03087 · v1 · pith:DXECXWBMnew · submitted 2018-02-09 · 🧮 math.CO

A Note on Intervals in the Hales-Jewett Theorem

Imre Leader , Eero Raty This is my paper
classification 🧮 math.CO
keywords hales-jewetttherelinemonochromaticnotetheoremactivealphabet
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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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  1. Linear orderings of combinatorial cubes

    math.CO 2019-06 unverdicted novelty 7.0

    Any linear ordering of [2]^n has a large subcube that is lexicographic; generalization bounds the number of possible orderings on subcubes of [k]^n by roughly (k-1)! / (2 (ln 2)^k).