## Abstract

Let I_{n} be the set of partial one-to-one transformations on the chain X_{n} = {1, 2, …, n} and, for each α in I_{n}, let h(α) = |Imα|, f(α) = |{x ∈ X_{n}: xα = x}| and w(α) = max(Imα). In this note, we obtain formulae involving binomial coeffcients of F(n; p, m, k) = |{α ∈ I_{n}: h(α) = p ∧f(α) = m ∧ w(α) = k}| and F(n; ·, m, k) = |{α ∈ I_{n}: f(α) = m ∧w(α) = k}| and analogous results on the set of partial derangements of I_{n} .

Original language | British English |
---|---|

Pages (from-to) | 78-91 |

Number of pages | 14 |

Journal | Algebra and Discrete Mathematics |

Volume | 33 |

Issue number | 2 |

DOIs | |

State | Published - 2022 |

## Keywords

- (left) waist of α
- (partial) derangement
- fix of α
- height of α
- partial one-to-one transformation
- permutation
- symmetric inverse monoid

## Fingerprint

Dive into the research topics of 'Further combinatorial results for the symmetric inverse monoid^{∗}'. Together they form a unique fingerprint.