Year: 2026
Type: article
Abstract: Two-sort species yield differential equations for functional digraphs of Cayley permutations. From these, we obtain an explicit formula for fixed-point-free Cayley permutations and prove that their proportion tends to 1 slash e $1/e$ 1 / e , as for permutations and endofunctions. Our approach also yields counting formulas when the functional digraph is a tree, forest, or connected.
Authors: Giulio Cerbai, Anders Claesson
Institution: University of Iceland
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162690835