Answers are grounded in this paper and cite their sources.
Study counts fixed-point-free Cayley permutations, indicating patterns in functional digraphs.
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.
No takes yet. Share an insight, caveat, or question.
Cerbai et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: