Egan's bound
For every n ≥ 4, S(n) \le n! + (n-1)! + (n-2)! + (n-3)! + n - 3
- Holds for
- n ≥ 4
- Announced
- Oct 20, 2018
- Proof
- Paper
- Coefficient of (n−3)!
- 1
By Greg Egan. Egan's construction adapts Aaron Williams's Hamiltonian-cycle construction.
Values
| n | At most |
|---|---|
| 4 | 34 |
| 5 | 154 |
| 6 | 873 |
| 7 | 5,908 |
| 8 | 46,205 |
| 9 | 408,966 |
| 10 | 4,037,047 |
| 11 | 43,948,808 |
| 12 | 522,910,089 |
| 13 | 6,749,568,010 |
| 14 | 93,924,230,411 |
Evidence
- Paper doi.org/10.1080/00029890.2021.1835384 Engen and Vatter, Amer. Math. Monthly 128 (2021), Theorem 2.3, 'for all n >= 4'