Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Signed Alternating-runs enumeration in Classical Weyl Groups   The alternating-runs polynomial enumerates alternating runs in the symmetric
group. There are three formulae for the number of permutations, $R_{n,k}$ in
$\mathfrak{S}_n$ with $k$ alternating runs, but all of them are complicated. We
show that when enumerated with sign taken into account, one gets a {\it neat
formula}. As a consequence, we get a near refinement of a result of Wilf on the
exponent of $(1+t)$ when it divides the alternating-runs polynomial in the
alternating group $\mathcal{A}_n$. Other applications include a moment-type
identity and enumeration of alternating permutations in $\mathcal{A}_n$.
Similar results are obtained for the type B and type D Coxeter groups.

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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph