Barber, B. Graphs and Combinatorics (2014) 30: 267. PDF Borg asked what happens to the Erdős-Ko-Rado theorem if we only count sets meeting some fixed set , and answered the question for , the size of the sets in the set family. This paper answers the question for , provided , the size of the …

# Author: babarber

## A note on balanced independent sets in the cube

Australas. J. Combin. 52 (2012), 205–207. PDF How large can an independent set in the discrete cube be if it contains equal numbers of sets of even and odd size? Take odd sets starting from the bottom of the cube, and even sets starting from the top. Proving that this works uses an isoperimetric inequality: …

## 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 …