Further combinatorial results for the symmetric inverse monoid

Abdallah Laradji, Abdullahi Umar

Research output: Contribution to journalArticlepeer-review


Let In be the set of partial one-to-one transformations on the chain Xn = {1, 2, …, n} and, for each α in In, let h(α) = |Imα|, f(α) = |{x ∈ Xn: xα = x}| and w(α) = max(Imα). In this note, we obtain formulae involving binomial coeffcients of F(n; p, m, k) = |{α ∈ In: h(α) = p ∧f(α) = m ∧ w(α) = k}| and F(n; ·, m, k) = |{α ∈ In: f(α) = m ∧w(α) = k}| and analogous results on the set of partial derangements of In .

Original languageEnglish
Pages (from-to)78-91
Number of pages14
JournalAlgebra and Discrete Mathematics
Issue number2
Publication statusPublished - Jan 1 2022
Externally publishedYes


  • (left) waist of α
  • (partial) derangement
  • fix of α
  • height of α
  • partial one-to-one transformation
  • permutation
  • symmetric inverse monoid

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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