Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The sorting index on colored permutations and even-signed permutations   We define a new statistic $\mathsf{sor}$ on the set of colored permutations
$\mathsf{G}_{r,n}$ and prove that it has the same distribution as the length
function. For the set of restricted colored permutations corresponding to the
arrangements of $n$ non-attacking rooks on a fixed Ferrers shape we show that
the following two sequences of set-valued statistics are joint equidistributed:
$(\ell,\mathsf{Rmil}^0,\mathsf{Rmil}^1,...,\mathsf{Rmil}^{r-1}$,
$\mathsf{Lmil}^0,\mathsf{Lmil}^1,...,\mathsf{Lmil}^{r-1}$,
$\mathsf{Lmal}^0,\mathsf{Lmal}^1,...,\mathsf{Lmal}^{r-1}$,
$\mathsf{Lmap}^0,\mathsf{Lmap}^1,...,\mathsf{Lmap}^{r-1})$ and
$(\mathsf{sor},\mathsf{Cyc}^0,\mathsf{Cyc}^{r-1},...,\mathsf{Cyc}^{1}$,
$\mathsf{Lmic}^0,\mathsf{Lmic}^{r-1},...,\mathsf{Lmic}^{1}$,
$\mathsf{Lmal}^0,\mathsf{Lmal}^1,...,\mathsf{Lmal}^{r-1}$,
$\mathsf{Lmap}^0,\mathsf{Lmap}^1,...,\mathsf{Lmap}^{r-1})$. Analogous results
are also obtained for Coxeter group of type $D$. Our results extend recent
results of Petersen, Chen-Gong-Guo and Poznanovi\'{c}.

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The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom