Enumeration of derangements with descents in prescribed positions
2009 ◽
Vol DMTCS Proceedings vol. AK,...
(Proceedings)
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International audience 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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2010 ◽
Vol DMTCS Proceedings vol. AN,...
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2010 ◽
Vol DMTCS Proceedings vol. AN,...
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2008 ◽
Vol DMTCS Proceedings vol. AJ,...
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2008 ◽
Vol DMTCS Proceedings vol. AJ,...
(Proceedings)
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2009 ◽
Vol Vol. 11 no. 1
(Combinatorics)
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2014 ◽
Vol Vol. 16 no. 1
(Combinatorics)
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2010 ◽
Vol DMTCS Proceedings vol. AM,...
(Proceedings)
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