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Upper and lower bounds for the density Hales-Jewett problem

This is a continuation of several threads from Tim Gowers’ massively collaborative mathematics project, “A combinatorial approach to density Hales-Jewett“, which I discussed in my previous post. For any positive integer n, let be the set of strings of length n consisting of 1s, 2s, and 3s, and define a combinatorial line to be a [...]
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