Enumeration of derangements with descents in prescribed positions
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

Author

Niklas Eriksen

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Ragnar Freij

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Johan Wästlund

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Electronic Journal of Combinatorics

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

Vol. 16 1 R32-

Subject Categories

Discrete Mathematics

More information

Created

10/6/2017