Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.09304 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912965273321472 |
|---|---|
| author | Cerbai, Giulio Claesson, Anders |
| author_facet | Cerbai, Giulio Claesson, Anders |
| contents | 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 $1/e$, as for permutations and endofunctions. Our approach also yields counting formulas when the functional digraph is a tree, forest, or connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting fixed-point-free Cayley permutations Cerbai, Giulio Claesson, Anders Combinatorics 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 $1/e$, as for permutations and endofunctions. Our approach also yields counting formulas when the functional digraph is a tree, forest, or connected. |
| title | Counting fixed-point-free Cayley permutations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.09304 |