Vertex-isoperimetric stability in the hypercube
Combinatorics
2019-10-17 v2
Abstract
Harper's Theorem states that, in a hypercube, among all sets of a given fixed size the Hamming balls have minimal closed neighbourhoods. In this paper we prove a stability-like result for Harper's Theorem: if the closed neighbourhood of a set is close to minimal in the hypercube, then the set must be very close to a Hamming ball around some vertex.
Cite
@article{arxiv.1808.02572,
title = {Vertex-isoperimetric stability in the hypercube},
author = {Michał Przykucki and Alexander Roberts},
journal= {arXiv preprint arXiv:1808.02572},
year = {2019}
}
Comments
18 pages