Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Permutations avoiding 312 and another pattern, Chebyshev polynomials and
  longest increasing subsequences   We study the longest increasing subsequence problem for random permutations
avoiding the pattern $312$ and another pattern $\tau$ under the uniform
probability distribution. We determine the exact and asymptotic formulas for
the average length of the longest increasing subsequences for such permutation
classes specifically when the pattern $\tau$ is monotone increasing or
decreasing, or any pattern of length four.

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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat