## 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 language | English |
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Title of host publication | FPSAC'09 - 21st International Conference on Formal Power Series and Algebraic Combinatorics |

Pages | 385-396 |

Number of pages | 12 |

Publication status | Published - 2009 |

MoE publication type | A4 Conference publication |

Event | International Conference on Formal Power Series and Algebraic Combinatorics - Linz, Austria Duration: 20 Jul 2009 → 24 Jul 2009 Conference number: 21 |

### Conference

Conference | International Conference on Formal Power Series and Algebraic Combinatorics |
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Abbreviated title | FPSAC |

Country/Territory | Austria |

City | Linz |

Period | 20/07/2009 → 24/07/2009 |

## Keywords

- Descent
- Fixed point
- Permutation statistic