On the number of subpermutations with fixed orbit size

Abdallah Laradji, Abdullahi Umar

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)447-460
Number of pages14
JournalArs Combinatoria
Volume109
Publication statusPublished - 2013

Fingerprint

Orbit
Exponential Generating Function
Nilpotency
Recurrence relation

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Laradji, A., & Umar, A. (2013). On the number of subpermutations with fixed orbit size. Ars Combinatoria, 109, 447-460.

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

In: Ars Combinatoria, Vol. 109, 2013, p. 447-460.

Research output: Contribution to journalArticle

Laradji, A & Umar, A 2013, 'On the number of subpermutations with fixed orbit size', Ars Combinatoria, vol. 109, pp. 447-460.
Laradji, Abdallah ; Umar, Abdullahi. / On the number of subpermutations with fixed orbit size. In: Ars Combinatoria. 2013 ; Vol. 109. pp. 447-460.
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