Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some combinatorial results on smooth permutations   We show that any smooth permutation $\sigma\in S_n$ is characterized by the
set ${\mathbf{C}}(\sigma)$ of transpositions and $3$-cycles in the Bruhat
interval $(S_n)_{\leq\sigma}$, and that $\sigma$ is the product (in a certain
order) of the transpositions in ${\mathbf{C}}(\sigma)$. We also characterize
the image of the map $\sigma\mapsto{\mathbf{C}}(\sigma)$. As an application, we
show that $\sigma$ is smooth if and only if the intersection of
$(S_n)_{\leq\sigma}$ with every conjugate of a parabolic subgroup of $S_n$
admits a maximum. This also gives another approach for enumerating smooth
permutations and subclasses thereof. Finally, we relate covexillary
permutations to smooth ones and rephrase the results in terms of the
(co)essential set in the sense of Fulton.

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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
5
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: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int