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{\bf Hilarion L. M. Faliharimalala and Jiang Zeng}
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{\bf Derangements and Euler's difference table for $C_\ell\wr S_n$}
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Euler's difference table associated to the sequence $\{n!\}$ leads
naturally to the counting formula for the derangements. In this paper
we study Euler's difference table associated to the sequence $\{\ell^n
n!\}$ and the generalized derangement problem.  For the coefficients
appearing in the later table we will give the combinatorial
interpretations in terms of two kinds of $k$-successions of the group
$C_\ell\wr S_n$.  In particular for $\ell=1$ we recover the known
results for the symmetric groups while for $\ell=2$ we obtain the
corresponding results for the hyperoctahedral groups.



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