Journal article, 2009

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.

descent

fixed point

Permutation statistic

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

1097-1440 (ISSN) 1077-8926 (eISSN)

Vol. 16 1 R32-Discrete Mathematics