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    An approximate isoperimetric inequality for r-sets 
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    An approximate isoperimetric inequality for r-sets

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    Submitted Version (141.8Kb)
    Journal
    Electronic Journal of Combinatorics
    ISSN
    1097-1440
    Metadata
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    Abstract
    We prove a vertex-isoperimetric inequality for [n]^(r), the set of all r-element subsets of {1,2,...,n}, where x,y \in [n]^(r) are adjacent if |x \Delta y|=2. 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. For \alpha bounded away from 0 and 1, this is sharp up to a constant factor (independent of n and r).
    Authors
    Christofides, D; Ellis, D; Keevash, P
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/15443
    Collections
    • Applied Mathematics [140]
    Licence information
    http://arxiv.org/abs/1203.3699
    Copyright statements
    © Authors
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