### Abstract

Consider an n-set, say X_{n} = {1,2,⋯, n}. An exponential generating function and recurrence relation for the number of subpermutations of X_{n}, whose orbits are of size at most k ≥ 0 are obtained. Similar results for the number of nilpotent subpermutations of nilpotency index at most k, and exactly k are also given, along with arithmetic and asypmtotic formulas for these numbers. 1 2.

Original language | English |
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Pages (from-to) | 447-460 |

Number of pages | 14 |

Journal | Ars Combinatoria |

Volume | 109 |

Publication status | Published - 2013 |

### Keywords

- Component
- Cycle
- Digraph
- Nilpotent
- Orbit
- Partial derangement
- Partial identity
- Partial one-one transformation
- Path
- Subpermutation

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'On the number of subpermutations with fixed orbit size'. Together they form a unique fingerprint.

## Cite this

Laradji, A., & Umar, A. (2013). On the number of subpermutations with fixed orbit size.

*Ars Combinatoria*,*109*, 447-460.