Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Restricted generating trees for weak orderings   Motivated by the study of pattern avoidance in the context of permutations
and ordered partitions, we consider the enumeration of weak-ordering chains
obtained as leaves of certain restricted rooted trees. A tree of order $n$ is
generated by inserting a new variable into each node at every step. A node
becomes a leaf either after $n$ steps or when a certain stopping condition is
met. In this paper we focus on conditions of size 2 ($x=y$, $x<y$, or $x\le y$)
and several conditions of size 3. Some of the cases considered here lead to the
study of descent statistics of certain `almost' pattern-avoiding permutations.

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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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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: cond-mat
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The categories of this paper are: stat