Some Ramsey results for the n-cube

Ron Graham; Jozsef Solymosi

Some Ramsey results for the n-cube

Combinatorics 2008-07-11 v1

Authors: Ron Graham , Jozsef Solymosi

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.

Keywords

ramsey theory cubic fourfolds differential geometry

Cite

@article{arxiv.0807.1557,
  title  = {Some Ramsey results for the n-cube},
  author = {Ron Graham and Jozsef Solymosi},
  journal= {arXiv preprint arXiv:0807.1557},
  year   = {2008}
}

Comments

10 pages, 5 figures

Related papers

View all related →