Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadrant Marked Mesh Patterns and the r-Stirling Numbers   Marked mesh patterns are a very general type of permutation pattern. We
examine a particular marked mesh pattern originally defined by Kitaev and
Remmel, and show that its generating function is described by the $r$-Stirling
numbers. We examine some ramifications of various properties of the
$r$-Stirling numbers for this generating function, and find (seemingly new)
formulas for the $r$-Stirling numbers in terms of the classical Stirling
numbers and harmonic numbers. We also answer some questions posed by Kitaev and
Remmel and show a connection to another mesh pattern introduced by Kitaev and
Liese.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org