On the number of subpermutations with fixed orbit size

Abdallah Laradji; Abdullahi Umar

On the number of subpermutations with fixed orbit size

Abdallah Laradji, Abdullahi Umar

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 - Apr 2013

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

Cite this

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title = "On the number of subpermutations with fixed orbit size",

abstract = "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.",

keywords = "Component, Cycle, Digraph, Nilpotent, Orbit, Partial derangement, Partial identity, Partial one-one transformation, Path, Subpermutation",

author = "Abdallah Laradji and Abdullahi Umar",

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T1 - On the number of subpermutations with fixed orbit size

AU - Laradji, Abdallah

AU - Umar, Abdullahi

PY - 2013/4

Y1 - 2013/4

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

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M3 - Article

AN - SCOPUS:84902131219

SN - 0381-7032

VL - 109

SP - 447

EP - 460

JO - Ars Combinatoria

JF - Ars Combinatoria

ER -

On the number of subpermutations with fixed orbit size

Abstract

Keywords

ASJC Scopus subject areas

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