W-0084
A superpermutation on 13 symbols, found by 
- Length
- 6,747,801,798
- Repeated permutations
- 1,797,404
- Received
- Nov 8, 202615:33:19 UTC
0123456789ABC0123456789AB0C123456789AB01C23456789AB012C3456789AB0123C456789AB01234C56789AB012345C6789AB0123456C789AB0123…
Windows
| 6,747,801,786 | windows of 13 consecutive letters | |
| = | 6,227,020,800 | distinct permutations |
| + | 1,797,404 | repeated permutations |
| + | 518,983,582 | windows that are not permutations |
Detours by weight
A step is the move from one permutation in the superpermutation to the next permutation in it, and its weight is the number of letters added in that move. A detour starts at a step that differs from the next step of the recursive construction, and ends at the first permutation after that whose next step has weight 1. The weight of a detour is the number of letters added in it. After each detour, we consider the recursive construction to begin again from scratch at the permutation where the detour ends.
| Weight | Detours |
|---|---|
| 1 | 0 |
| 2 | 0 |
| 3 | 11,695,375 |
| 4 | 3,921 |
| 5 | 1,503 |
| 6 | 1,232 |
| 7 | 341 |
| 8 | 1,358 |
| 9 | 453 |
| 10 | 661 |
| 11 | 104 |
| 12 | 142 |
| 13 | 5 |
How it was found
From the submitter
Jay Pantone's 43/80 construction with my own selection of closed trails (different ones than in his words). The order and the cuts of the trails come from my segment insertion search on the GPU, plus two moves from the superpermutators group: William Echols's re-opening of a run of consecutive trails and Theo H.'s moving of a trail with a new phase. Published on 25 Oct 2026 in jhalfar/superpermutations as words/superpermutation-13-6747801798.spra.xz (Theo H.'s SPRA format).
Made with Claude (Opus 5.5) in Claude Code. I decide what to try, Claude writes the code and runs the searches.
Download
Learn about the Detour file format
Download Detour (.detour) 222.2 kB, or 6.7 GB decoded