An isoperimetric inequality for Hamming balls and local expansion in hypercubes

Zilin Jiang; Amir Yehudayoff

doi: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

Access to Document

10.37236/9860

Cite this

@article{a6852e82b3c9412faef244b43228cd15,

title = "An isoperimetric inequality for Hamming balls and local expansion in hypercubes",

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.",

author = "Zilin Jiang and Amir Yehudayoff",

note = "Publisher Copyright: {\textcopyright}The authors.",

year = "2022",

month = jan,

day = "28",

doi = "10.37236/9860",

language = "الإنجليزيّة",

volume = "29",

journal = "Electronic Journal of Combinatorics",

issn = "1077-8926",

publisher = "Electronic Journal of Combinatorics",

number = "1",

}

TY - JOUR

T1 - An isoperimetric inequality for Hamming balls and local expansion in hypercubes

AU - Jiang, Zilin

AU - Yehudayoff, Amir

PY - 2022/1/28

Y1 - 2022/1/28

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=85123547222&partnerID=8YFLogxK

U2 - 10.37236/9860

DO - 10.37236/9860

M3 - مقالة

SN - 1077-8926

VL - 29

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

IS - 1

M1 - 1

ER -

An isoperimetric inequality for Hamming balls and local expansion in hypercubes

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this