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{\bf Niklas Eriksen, Ragnar Freij and Johan W\"astlund}
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{\bf Enumeration of Derangements with Descents in Prescribed Positions}
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We enumerate derangements with descents in prescribed positions. A
generating function was given by Guo-Niu Han and Guoce Xin in 2007. We
give a combinatorial proof of this result, and derive several explicit
formulas. To this end, we consider fixed point $\lambda$-coloured
permutations, which are easily enumerated. Several formulae regarding
these numbers are given, as well as a generalisation of Euler's
difference tables. We also prove that except in a trivial special
case, if a permutation $\pi$ is chosen uniformly among all
permutations on $n$ elements, the events that $\pi$ has descents in a
set $S$ of positions, and that $\pi$ is a derangement, are positively
correlated.



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