Abstract
Ramras conjectured that the maximum size of an independent set in the discrete cube Qn containing equal numbers of sets of even and odd size is 2n−1 − \binom {n−1} {(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.
| Original language | English |
|---|---|
| Pages (from-to) | 205-207 |
| Number of pages | 3 |
| Journal | Australasian Journal of Combinatorics |
| Volume | 52 |
| Publication status | Published - Feb 2012 |