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Namely, if \\mathcal{A} \\subset [n]^(r) with |\\mathcal{A}|=\\alpha {n \\choose r}, then the vertex-boundary b(\\mathcal{A}) satisfies |b(\\mathcal{A})| \\geq c\\sqrt{\\frac{n}{r(n-r)}} \\alpha(1-\\alpha) {n \\choose r}, where c is a positive absolute constant. 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