Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An isoperimetric inequality for antipodal subsets of the discrete cube   A family of subsets of $\{1,2,\ldots,n\}$ is said to be {\em antipodal} if it
is closed under taking complements. We prove a best-possible isoperimetric
inequality for antipodal families of subsets of $\{1,2,\ldots,n\}$. Our
inequality implies that for any $k \in \mathbb{N}$, among all such families of
size $2^k$, a family consisting of the union of a $(k-1)$-dimensional subcube
and its antipode has the smallest possible edge boundary.

33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys