### 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 |
---|---|

Pages (from-to) | 447-460 |

Number of pages | 14 |

Journal | Ars Combinatoria |

Volume | 109 |

Publication status | Published - 2013 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Ars Combinatoria*,

*109*, 447-460.

**On the number of subpermutations with fixed orbit size.** / Laradji, Abdallah; Umar, Abdullahi.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - On the number of subpermutations with fixed orbit size

AU - Laradji, Abdallah

AU - Umar, Abdullahi

PY - 2013

Y1 - 2013

N2 - Consider an n-set, say Xn = {1,2,⋯, n}. An exponential generating function and recurrence relation for the number of subpermutations of Xn, 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.

AB - Consider an n-set, say Xn = {1,2,⋯, n}. An exponential generating function and recurrence relation for the number of subpermutations of Xn, 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.

KW - Component

KW - Cycle

KW - Digraph

KW - Nilpotent

KW - Orbit

KW - Partial derangement

KW - Partial identity

KW - Partial one-one transformation

KW - Path

KW - Subpermutation

UR - http://www.scopus.com/inward/record.url?scp=84902131219&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902131219&partnerID=8YFLogxK

M3 - Article

VL - 109

SP - 447

EP - 460

JO - Ars Combinatoria

JF - Ars Combinatoria

SN - 0381-7032

ER -