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arXiv · 0807.1557

Some Ramsey results for the n-cube

Ron Graham·Jozsef Solymosi
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Abstract

In this note we establish a Ramsey-type result for certain subsets of the $n$-dimensional cube. This can then be applied to obtain reasonable bounds on various related structures, such as (partial) Hales-Jewett lines for alphabets of sized 3 and 4, Hilbert cubes in sets of real numbers with small sumsets, "corner" in the integer lattice in the plane, and 3-term geometric progressions in integers.

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Ron Graham, Jozsef Solymosi. 2008-07-09. Some Ramsey results for the n-cube. https://arxiv.org/abs/0807.1557

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