= Vertex-isoperimetric inequality in the discrete cube
{title2=$|N(\mathcal A)|\geq|N(I_{|\mathcal A|})|$}
= Harper theorem
{c}
{synonym}
For the <Boolean hypercube>, the <initial segment> of the <simplicial order on the discrete cube> minimizes the size of the closed <vertex neighbourhood> among families of a given size. Equivalently, it minimizes the <external vertex boundary>. This is a vertex assertion, distinct from the <edge-isoperimetric inequality in the discrete cube>.
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