Enumeration of derangements with descents in prescribed positions

Details Enumeration of derangements with descents in prescribed positions Enumeration of derangements with descents in prescribed positions

2008-11-12

arxiv.org/abs/0811.1925v1

Mathematics

Combinatorics

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Enumeration of derangements with descents in prescribed positions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Enumeration of derangements with descents in prescribed positions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Enumeration of derangements with descents in prescribed positions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-101296