Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Signed Euler-Mahonian identities   A relationship between signed Eulerian polynomials and the classical Eulerian
polynomials on $\mathfrak{S}_n$ was given by D\'{e}sarm\'{e}nien and Foata in
1992, and a refined version, called signed Euler-Mahonian identity, together
with a bijective proof were proposed by Wachs in the same year. By generalizing
this bijection, in this paper we extend the above results to the Coxeter groups
of types $B_n$, $D_n$, and the complex reflection group $G(r,1,n)$, where the
`sign' is taken to be any one-dimensional character. Some obtained identities
can be further restricted on some particular set of permutations. We also
derive some new interesting sign-balance polynomials for types $B_n$ and $D_n$.

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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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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: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: physics