### 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) |
---|---|

Pages (from-to) | 311-328 |

Number of pages | 18 |

Journal | Journal of Combinatorial Theory, Series A |

Volume | 64 |

Issue number | 2 |

DOIs | |

State | Published - 1993 |

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### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory, Series A*,

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

**Descent classes of permutations with a given number of fixed points.** / Désarménien, Jacques; Galloway, Michelle L.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory, Series A*, vol. 64, no. 2, pp. 311-328. https://doi.org/10.1016/0097-3165(93)90100-M

}

TY - JOUR

T1 - Descent classes of permutations with a given number of fixed points

AU - Désarménien, Jacques

AU - Galloway, Michelle L

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38249001068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249001068&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(93)90100-M

DO - 10.1016/0097-3165(93)90100-M

M3 - Article

AN - SCOPUS:38249001068

VL - 64

SP - 311

EP - 328

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -