Symmetric colorings of Hales-Jewett cubes coincide with one-weight colorings, reducing the symmetric lower-bound problem to 1D Gallai homothety coloring and yielding HJ(3,3)≥22 and HJ(4,2)≥14.
Van der Waerden's Theorem on Homothetic copies of {1,1+s, 1+s+t}
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abstract
T.C. Brown, B.M. Landman and M. Mishna raised a problem on monochromatic homothetic copies of {1,1+s, 1+s+t}. We solved the problem completely.
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math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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One-Weight Colorings, the Symmetric Class, and Lower Bounds for Hales--Jewett Numbers
Symmetric colorings of Hales-Jewett cubes coincide with one-weight colorings, reducing the symmetric lower-bound problem to 1D Gallai homothety coloring and yielding HJ(3,3)≥22 and HJ(4,2)≥14.