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.
A construction for partitions which avoid long arithmetic progressions
2 Pith papers cite this work. Polarity classification is still indexing.
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H(k)^{1/k}/k = Ω(k/log k) as k→∞, resolving the positive direction of Erdős-Graham problem #190.
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A resolution of Erd\H{o}s Problem #190 via Erd\H{o}s-Lov\'asz, BCT, and Baker-Harman-Pintz
H(k)^{1/k}/k = Ω(k/log k) as k→∞, resolving the positive direction of Erdős-Graham problem #190.