Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intersecting Families of Permutations   A set of permutations $I \subset S_n$ is said to be {\em k-intersecting} if
any two permutations in $I$ agree on at least $k$ points. We show that for any
$k \in \mathbb{N}$, if $n$ is sufficiently large depending on $k$, then the
largest $k$-intersecting subsets of $S_n$ are cosets of stabilizers of $k$
points, proving a conjecture of Deza and Frankl. We also prove a similar result
concerning $k$-cross-intersecting subsets. Our proofs are based on eigenvalue
techniques and the representation theory of the symmetric group.

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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: q-alg