Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Paths and Packings in Halves   It is shown that one can count $k$-edge paths in an $n$-vertex graph and
$m$-set $k$-packings on an $n$-element universe, respectively, in time ${n
\choose k/2}$ and ${n \choose mk/2}$, up to a factor polynomial in $n$, $k$,
and $m$; in polynomial space, the bounds hold if multiplied by $3^{k/2}$ or
$5^{mk/2}$, respectively. These are implications of a more general result:
given two set families on an $n$-element universe, one can count the disjoint
pairs of sets in the Cartesian product of the two families with $\nO(n \ell)$
basic operations, where $\ell$ is the number of members in the two families and
their subsets.

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The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph