One paper in Euclidean Ramsey theory is “Transitive sets in Euclidean Ramsey theory” by Imre Leader, Paul A. Russell and Mark Walters. A set is transitive if its symmetry group of isometries is transitive. The paper looks at the question what if only transitive sets are Ramsey. It is known that Ramsey sets are spherical and it has been conjectured that all spherical sets are Ramsey. The paper shows that the conjectures are not equivalent that there exist sets that are spherical and cannot be embedded in any transitive set. It also looks at equivalent forms of the statement all transiive sets are Ramsey. It is here. I may talk further about the questions raised in this paper in future posts as there are some other papers written in response to these questions
Archive for June, 2015
I have just logged on. I have not posted in over a year. I think a while back I posted about new developments in the field. I might do that again. There are some things that I want to talk about in Euclidean Ramsey theory. I hope to get my next post here faster than the 18 month gap between this post and the last.