Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge Isoperimetric Inequalities for Powers of the Hypercube   For positive integers $n$ and $r$, we let $Q_n^r$ denote the $r$th power of
the $n$-dimensional discrete hypercube graph, i.e., the graph with vertex-set
$\{0,1\}^n$, where two 0-1 vectors are joined if they are Hamming distance at
most $r$ apart. We study edge isoperimetric inequalities for this graph.
Harper, Bernstein, Lindsey and Hart proved a best-possible edge isoperimetric
inequality for this graph in the case $r=1$. For each $r \geq 2$, we obtain an
edge isoperimetric inequality for $Q_n^r$; our inequality is tight up to a
constant factor depending only upon $r$. Our techniques also yield an edge
isoperimetric inequality for the `Kleitman-West graph' (the graph whose
vertices are all the $k$-element subsets of $\{1,2,\ldots,n\}$, where two
$k$-element sets have an edge between them if they have symmetric difference of
size two); this inequality is sharp up to a factor of $2+o(1)$ for sets of size
${n -s \choose k-s}$, where $k=o(n)$ and $s \in \mathbb{N}$.

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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int