### Abstract

A desarrangement is a permutation whose first ascent is even. The first author introduced this class of permutations for the purpose of combinatorially explaining a standard recurrence relation for the number of derangements of n elements. He gave a nice bijection between derangements and desarrangements. Here we extend his bijection to obtain more refined enumeration results relating derangements and desarrangements. In particular, we construct a bijection between descent classes of derangements and descent classes of desarrangements. The following monotonicity result is a consequence of this correspondence: In any (nontrivial) descent class the number of permutations with exactly k fixed points decreases as k increases.

Original language | English (US) |
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Pages (from-to) | 311-328 |

Number of pages | 18 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 64 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1993 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

*Journal of Combinatorial Theory, Series A*,

*64*(2), 311-328. https://doi.org/10.1016/0097-3165(93)90100-M