Journal of Integer Sequences, Vol. 25 (2022), Article 22.8.6 |

Department of Computer Science

Ben-Gurion University of the Negev

David Ben-Gurion Blvd 1

Be'er Sheva

Israel

**Abstract:**

Recently, Defant and Propp defined the degree of noninvertibility of a function
between two finite nonempty sets by
. We obtain an exact formula for the expected degree of noninvertibility of the composition of functions for every
. 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.

(Concerned with sequences A074909 A208250.)

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.

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