Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic aspects of increasing subsequences   We present a number of results relating partial Cauchy-Littlewood sums,
integrals over the compact classical groups, and increasing subsequences of
permutations. These include: integral formulae for the distribution of the
longest increasing subsequence of a random involution with constrained number
of fixed points; new formulae for partial Cauchy-Littlewood sums, as well as
new proofs of old formulae; relations of these expressions to orthogonal
polynomials on the unit circle; and explicit bases for invariant spaces of the
classical groups, together with appropriate generalizations of the
straightening algorithm.

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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph