Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903601 | European Journal of Combinatorics | 2018 | 6 Pages |
Abstract
We say a family of subsets of {1,2,â¦,n} is antipodal if it is closed under taking complements. We prove a best-possible isoperimetric inequality for antipodal families of subsets of {1,2,â¦,n} (of any size). Our inequality implies that for any kâN, among all such families of size 2k, a family consisting of the union of two antipodal (kâ1)-dimensional subcubes has the smallest possible edge boundary.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
David Ellis, Imre Leader,