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Enumeration of derangements with descents in prescribed positions

Författare och institution:
Niklas Eriksen (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); Ragnar Freij (Institutionen för matematiska vetenskaper, Chalmers/GU); Johan Wästlund (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Publicerad i:
Electronic Journal of Combinatorics, 16 ( 1 ) s. R32
ISSN:
1077-8926
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2009
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik ->
Diskret matematik
Nyckelord:
Permutation statistic, fixed point, descent
Postens nummer:
94521
Ingår i post nr:
Posten skapad:
2009-05-29 10:54
Posten ändrad:
2016-07-26 11:01

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