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arXiv · 1807.00626

An isoperimetric inequality for Hamming balls and local expansion in hypercubes

Zilin Jiang·Amir Yehudayoff
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Abstract

We prove a vertex isoperimetric inequality for the $n$-dimensional Hamming ball $\mathcal{B}_n(R)$ of radius $R$. The isoperimetric inequality is sharp up to a constant factor for sets that are comparable to $\mathcal{B}_n(R)$ in size. A key step in the proof is a local expansion phenomenon in hypercubes.

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Zilin Jiang, Amir Yehudayoff. 2022-02-08. An isoperimetric inequality for Hamming balls and local expansion in hypercubes. https://doi.org/10.37236/9860

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