Some Ramsey-type results for the n-cube |
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| Authors: | Ron Graham |
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| Institution: | a University of California, San Diego, United States
b University of British Columbia, Vancouver, Canada |
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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 sizes 3 and 4, Hilbert cubes in sets of real numbers with small sumsets, “corners” in the integer lattice in the plane, and 3-term integer geometric progressions. |
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| Keywords: | Ramsey Theory Monochromatic corners Hales-Jewett Theorem |
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