Enumeration of derangements with descents in prescribed positions
Artikel i vetenskaplig tidskrift, 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

Författare

Niklas Eriksen

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Ragnar Freij

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Johan Wästlund

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Electronic Journal of Combinatorics

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

Vol. 16 1 R32-

Ämneskategorier

Diskret matematik