The Expected Degree of Noninvertibility of Compositions of Functions

Sela Fried

Research output: Contribution to journalArticlepeer-review


Recently, Defant and Propp defined the degree of noninvertibility of a function f: X → Y between two finite nonempty sets by deg(f) =1 ∑ |X| x∈X|f−1 (f(x))|. We obtain an exact formula for the expected degree of noninvertibility of the composition of t functions for every t ∈ N. Subsequently, we use the expected value to quantify a strengthening of a sort of a submultiplicativity property of the degree of noninvertibil-ity. Finally, we generalize an equivalent formulation of the degree of noninvertibility and obtain a combinatorial identity involving the Stirling numbers of the first and second kind.

Original languageEnglish
Article number22.8.6
JournalJournal of Integer Sequences
Issue number8
StatePublished - 1 Jan 2022


  • Stirling number
  • degree of noninvertibility
  • dynamical system

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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