%0 Journal Article
%T Some Ramsey results for the n-cube
%A Ron Graham
%A Jozsef Solymosi
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0807.1557v1