Description
Abstract: A classic result in Euclidean Ramsey Theory states that for every infinite set of points M, there exists a two-coloring of the Euclidean space (of an arbitrary dimension) such that no isometric copy of M is monochromatic. We will see that the direct analogue of this result also holds in ell_p planes for all real p>1, but fails for all polygonal norms. In case p=∞, we will even show that there exists a single infinite set M such that some of its isometric copies are monochromatic whenever an n-dimensional space is colored in less than log(n) colors.