## Abstract

Ramras conjectured that the maximum size of an independent set in the discrete cube

*Q*containing equal numbers of sets of even and odd size is 2_{n}^{n−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 |
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Pages (from-to) | 205-207 |

Number of pages | 3 |

Journal | Australasian Journal of Combinatorics |

Volume | 52 |

Publication status | Published - Feb 2012 |