Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The alternating run polynomials of permutations   In this paper, we first consider a generalization of the David-Barton
identity which relate the alternating run polynomials to Eulerian polynomials.
By using context-free grammars, we then present a combinatorial interpretation
of a family of q-alternating run polynomials. Furthermore, we introduce the
definition of semi-gamma-positive polynomial and we show the
semi-gamma-positivity of the alternating run polynomials of dual Stirling
permutations. A connection between the up-down run polynomials of permutations
and the alternating run polynomials of dual Stirling permutations is
established.

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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom