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

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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.