Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to decompose a permutation into a pair of labeled Dyck paths by
  playing a game   We give a bijection between permutations of length 2n and certain pairs of
Dyck paths with labels on the down steps. The bijection arises from a game in
which two players alternate selecting from a set of 2n items: the permutation
encodes the players' preference ordering of the items, and the Dyck paths
encode the order in which items are selected under optimal play. We enumerate
permutations by certain statistics, AA inversions and BB inversions, which have
natural interpretations in terms of the game. We give new proofs of classical
identities such as \sum_p \prod_{i=1}^n q^{h_i -1} [h_i]_q = [1]_q [3]_q ...
[2n-1]_q where the sum is over all Dyck paths p of length 2n, and the h_i are
the heights of the down steps of p.

10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex