English

A note on balanced independent sets in the cube

Combinatorics 2012-10-16 v1

Abstract

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.

Cite

@article{arxiv.1210.4029,
  title  = {A note on balanced independent sets in the cube},
  author = {Ben Barber},
  journal= {arXiv preprint arXiv:1210.4029},
  year   = {2012}
}

Comments

2 pages

R2 v1 2026-06-21T22:21:52.216Z