The 4chan bound
For every n, S(n) \ge n! + (n-1)! + (n-2)! + n - 3
- Holds for
- all n
- Announced
- Sep 17, 2011
- Proof
- Paper
- Coefficient of (n−3)!
- 0
By Anonymous 4chan poster, Robin Houston, Jay Pantone 
Values
| n | At least |
|---|---|
| 3 | 9 |
| 4 | 33 |
| 5 | 152 |
| 6 | 867 |
| 7 | 5,884 |
| 8 | 46,085 |
| 9 | 408,246 |
| 10 | 4,032,007 |
| 11 | 43,908,488 |
| 12 | 522,547,209 |
| 13 | 6,745,939,210 |
| 14 | 93,884,313,611 |
Evidence
- Preprint oeis.org/A180632/a180632.pdf Anonymous 4chan Poster, Houston, Pantone, Vatter, 'A lower bound on the length of the shortest superpattern', October 25, 2018, hosted at OEIS
- Paper doi.org/10.1080/00029890.2021.1835384 Engen and Vatter, 'Containing All Permutations', Amer. Math. Monthly 128 (2021) 4-24, Theorem 2.5 (arXiv:1810.08252)
- Computer check github.com/ccd0/superpermutations Coq formalization of the argument (2015–2018)