Graham-Rothschild via Hales-Jewett - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T00:08:23Z http://mathoverflow.net/feeds/question/108335 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108335/graham-rothschild-via-hales-jewett Graham-Rothschild via Hales-Jewett Fedor Petrov 2012-09-28T12:02:57Z 2012-10-14T09:04:21Z <p>I am currently reading the recent preprint of Dodos, Kanellopoulos, Tyros, where the ambitiously short proof of Density Hales Jewett theorem is provided. The important ingredient is Graham-Rothschild theorem. The authors say that it follows from the HJ by some standard Ramsey arguments, but I can not find them myself, at least immediately. Is it written anywhere? Original paper of Graham and Rothschild looks too long for being used in "simple self-contained proof" of anything. Polymath's DHJ proof does not use GR at all, on first glance.</p> http://mathoverflow.net/questions/108335/graham-rothschild-via-hales-jewett/109518#109518 Answer by T.Karageorgos for Graham-Rothschild via Hales-Jewett T.Karageorgos 2012-10-13T07:18:41Z 2012-10-14T09:04:21Z <p>In Randall - McCutcheon's book "Elemental methods in ergodic Ramsey theory" a stronger version of GR's theorem is prooved about block subspaces (theorem 2.4.1). The only theorems you need in order to proove it is Hales-Jewett and Folkman's theorem (about finite unions which you can proove using Hales - Jewett theorem again).</p> <p>Another proof is given in Graham - Rothschild -Spencer book about Ramsey theory using HJ and linear algebra.</p>