An isoperimetric inequality for Hamming balls and local expansion in hypercubes

Zilin Jiang; Amir Yehudayoff

doi:https://doi.org/10.37236/9860

An isoperimetric inequality for Hamming balls and local expansion in hypercubes

Zilin Jiang, Amir Yehudayoff

Mathematics

Technion - Israel Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Article number	1
Journal	Electronic Journal of Combinatorics
Volume	29
Issue number	1
DOIs	https://doi.org/10.37236/9860
State	Published - 28 Jan 2022

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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abstract = "We prove a vertex isoperimetric inequality for the n-dimensional Hamming ball Bn(R) of radius R. The isoperimetric inequality is sharp up to a constant factor for sets that are comparable to Bn(R) in size. A key step in the proof is a local expansion phenomenon in hypercubes.",

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

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An isoperimetric inequality for Hamming balls and local expansion in hypercubes

Abstract

All Science Journal Classification (ASJC) codes

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