W-0079
A superpermutation on 11 symbols, found by Jay Pantone 
- Length
- 43,930,548
- Repeated occurrences
- 19,768
- Received
- Oct 28, 202623:30:26 UTC
0123456789A01234567890A12345678901A23456789012A34567890123A45678901234A56789012345A67890123456A78901234567A89012345678A9…
Windows
| 43,930,538 | windows of 11 consecutive letters | |
| = | 39,916,800 | distinct permutations, all 11! of them |
| + | 19,768 | repeated occurrences of a permutation |
| + | 3,993,970 | windows that are not permutations |
How it was found
This word was obtained by optimizing Jakub Halfar’s selection X and starting arrangement within my superpermutation construction. We varied the relabelings and arrangement of its blocks, then used dynamic programming to optimize where the cyclic pieces were opened, minimizing the letters needed to join them.
Checking
Total check time: 2 s, including preparation but not time in the queue.
| Program | Source | Result | Time |
|---|---|---|---|
| classcheck | 41928cce | all 39,916,800 permutations appear, by rotation class | under 1 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | 1 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | under 1 s |
Download
Download Detour (.detour) 8.5 kB, or 43.9 MB decoded
# check it yourself
detour decode W-0079.detour - | tr -d '\n' | shasum -a 256
tar xzf checkers-rs-source.tar.gz && cd checkers-rs && cargo build --release --locked
./target/release/classcheck 11 ../W-0079.detour 43930548
./target/release/bitmapcheck 11 ../W-0079.detour 43930548
./target/release/wordhash 11 ../W-0079.detour 43930548
Decoding needs detour; see the Detour format for how to build and install it. The checkers are in checkers-rs-source.tar.gz, which needs Rust 1.89 or later; each one decodes the file itself, so the word is never written out.
The file's header gives n = 11 and sync exponent 0. The file has 513,603 tokens: 1 START and 513,602 deviations. Deviations by weight, from 1 to 11: 19,768 · 136,619 · 357,010 · 9 · 63 · 40 · 25 · 44 · 18 · 4 · 2.