Enumeration of derangements with descents in prescribed positions

Niklas Eriksen*, Ragnar Freij, Johan Wästlund

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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 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.

Original languageEnglish
Title of host publicationFPSAC'09 - 21st International Conference on Formal Power Series and Algebraic Combinatorics
Pages385-396
Number of pages12
Publication statusPublished - 2009
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Formal Power Series and Algebraic Combinatorics - Linz, Austria
Duration: 20 Jul 200924 Jul 2009
Conference number: 21

Conference

ConferenceInternational Conference on Formal Power Series and Algebraic Combinatorics
Abbreviated titleFPSAC
CountryAustria
CityLinz
Period20/07/200924/07/2009

Keywords

  • Descent
  • Fixed point
  • Permutation statistic

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