Enumeration of derangements with descents in prescribed positions
| dc.creator | Eriksen, Niklas | |
| dc.creator | Freij, Ragnar | |
| dc.creator | Wastlund, Johan | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:44Z | |
| dc.date.available | 2026-07-07T10:17:44Z | |
| dc.description | 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 $λ$-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 $π$ is chosen uniformly among all permutations on $n$ elements, the events that $π$ has descents in a set $S$ of positions, and that $π$ is a derangement, are positively correlated. | |
| dc.identifier | https://arxiv.org/abs/0811.1925 | |
| dc.identifier | http://arxiv.org/abs/0811.1925 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173957 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A05; 05A15 | |
| dc.title | Enumeration of derangements with descents in prescribed positions | |
| dc.type | text |