Recently, Defant and Propp defined the degree of noninvertibility of a function
![$f\colon X\to Y$](abs/img2.svg)
between two finite nonempty sets by
![$\deg(f)=\frac{1}{\vert X\vert}\sum_{x\in X}\vert f^{-1}(f(x))\vert$](abs/img3.svg)
. We obtain an exact formula for the expected degree of noninvertibility of the composition of
![$t$](abs/img4.svg)
functions for every
![$t\in \mathbb{N}$](abs/img5.svg)
. Subsequently, we use the expected value to quantify a strengthening of a sort of a submultiplicativity property of the degree of noninvertibility. 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.
Received September 8 2022; revised version received October 10 2022; October 12 2022;
October 21 2022.
Published in Journal of Integer Sequences,
October 25 2022.