Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Longest alternating subsequences of permutations   The length is(w) of the longest increasing subsequence of a permutation w in
the symmetric group S_n has been the object of much investigation. We develop
comparable results for the length as(w) of the longest alternating subsequence
of w, where a sequence a,b,c,d,... is alternating if a>b<c>d<.... For instance,
the expected value (mean) of as(w) for w in S_n is exactly (4n+1)/6 if n>1.

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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc