Geodesic
Derangements and Euler's difference table for \(C_{l} \wr S_{n}\)
The electronic journal of combinatorics, Tome 15 (2008)
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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.
DOI : 10.37236/789
Classification : 05A18, 05A15, 05A30 
@article{10_37236_789,
     author = {Hilarion L. M. Faliharimalala and Jiang Zeng},
     title = {Derangements and {Euler's} difference table for {\(C_{l}} \wr {S_{n}\)}},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/789},
     zbl = {1181.05013},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/789/}
}
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Hilarion L. M. Faliharimalala; Jiang Zeng. Derangements and Euler's difference table for \(C_{l} \wr S_{n}\). The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/789

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