Paper for Polymath1 Project

I mentioned the polymath1 project in my previous post. I am now involved in writing a paper for this project.  The writing has just started  in the last couple of days.  It seems to be going well so far.  I will be writing more as the writing progresses. The working title is “Density Hales Jewett and Moser numbers in low Dimensions.”

Introduction

This is my first post in this blog. It will be about Euclidean Ramsey theory and possibly about related areas that I am working on. The related areass I am currently working on are the polymath1 project  and more specifically the number of points an n-dimensional cube of side three can have without forming a geometric line. This is a spinoff from the main project of finding a combinatorial proof of the density Hales Jewitt theorem for n=3 and generalizing that to higher n.