Enumeration of Derangements with Descents in Prescribed Positions
2009 (English)In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 16, no 1, R32Article in journal (Refereed) Published
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, aswell 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 \p$ is a derangement, are positively correlated.
Place, publisher, year, edition, pages
2009. Vol. 16, no 1, R32
Research subject Mathematics
IdentifiersURN: urn:nbn:se:oru:diva-39115ISI: 000263841800002ScopusID: 2-s2.0-61849142920OAI: oai:DiVA.org:oru-39115DiVA: diva2:766789