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Enumeration of Derangements with Descents in Prescribed Positions
Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden.ORCID iD: 0000-0002-6444-7878
Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden.
Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden.
2009 (English)In: The Electronic Journal of Combinatorics, ISSN 1077-8926, Vol. 16, no 1, R32Article in journal (Refereed) Published
Abstract [en]

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
National Category
Discrete Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-39115ISI: 000263841800002Scopus ID: 2-s2.0-61849142920OAI: oai:DiVA.org:oru-39115DiVA: diva2:766789
Available from: 2014-11-28 Created: 2014-11-28 Last updated: 2015-08-05Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf