A note on balanced independent sets in the cube

Ben Barber

Published 2012-10-15Version 1

Ramras conjectured that the maximum size of an independent set in the discrete cube containing equal numbers of sets of even and odd size is 2^(n-1) - (n-1 choose (n-1)/2) when n is odd. We prove this conjecture, and find the analogous bound when n is even. The result follows from an isoperimetric inequality in the cube.