The Namer-Claimer game

Consider the following game played on the integers from to .  In each round Namer names a forbidden distance , then Claimer claims a subset of that does not contain any two integers at distance .  After finitely many rounds, Claimer will have claimed sets that cover the whole of , at which point the …

Nowhere zero 6-flows

A flow on a graph is an assignment to each edge of of a direction and a non-negative integer (the flow in that edge) such that the flows into and out of each vertex agree.  A flow is nowhere zero if every edge is carrying a positive flow and (confusingly) it is a -flow if the flows …

Piecewise syndetic and van der Waerden

Joel Moreira has just proved that whenever the natural numbers are finitely coloured we can find and such that , and are all the same colour.  He actually proves a much more general result via links to topological dynamics, but he includes a direct proof of this special case assuming only a consequence of van der Waerden’s …