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arXiv · 1210.4029

A note on balanced independent sets in the cube

Ben Barber
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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.

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Ben Barber. 2012-10-15. A note on balanced independent sets in the cube. https://arxiv.org/abs/1210.4029

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