Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Major index over descent for pattern-avoiding permutations   An open conjecture in pattern avoidance theory is that the distribution of
the major index among 321-avoiding permutations is distributed unimodally. We
construct a formula for this distribution, and in the case of 2 descents prove
unimodality, with unimodality for 3 through 5 descents likely being little more
complicated. The formula refines the $q$-analogue of the Frame-Robinson-Thrall
hooklength formula for two-rowed partitions, and in the latter part of the
paper we discuss another theorem of the same type, and further exploration
toward this question. We also give observations on the analogous behaviors for
other permutation patterns of length 3.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an