An isoperimetric inequality for Hamming balls and local expansion in hypercubes

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.

19 pages, 1 figure, published in the Electronic Journal of Combinatorics

References in corpus (1)

• An approximate isoperimetric inequality for r-sets