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Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 11 / 1 / ii

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2014 iii Paper 11 1
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A down-set in the Boolean lattice is a family closed under taking subsets. Restricting the minimization to down-sets cannot decrease the minimum from the edge-isoperimetric inequality in the discrete cube.
The coordinate subcube consisting of all subsets of a fixed k-element set is itself a down-set and attains that minimum. Thus
g(2k)=2k(n−k)​.
(1)

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