W-0051
A superpermutation on 12 symbols, found by Theo H.. It is listed as a notable word: it ties W-0049, the record at the time.
- Length
- 522,745,531
- Repeated occurrences
- 169,350
- Announced
- Oct 5, 2026
0123456789AB0123456789A0B123456789A01B23456789A012B3456789A0123B456789A01234B56789A012345B6789A0123456B789A01234567B89A0…
Why it is listed
Theo H.'s dynamic programme for where each closed trail opens, run on Halfar's 522,745,538; ties Halfar's word committed earlier.
Windows
| 522,745,520 | windows of 12 consecutive letters | |
| = | 479,001,600 | distinct permutations, all 12! of them |
| + | 169,350 | repeated occurrences of a permutation |
| + | 43,574,570 | windows that are not permutations |
How it was found
Theo H.'s dynamic programme for where each closed trail opens, run on Halfar's 522,745,538; ties Halfar's word committed earlier.
Checking
Total check time: 8 s, including preparation but not time in the queue.
| Program | Source | Result | Time |
|---|---|---|---|
| classcheck | 41928cce | all 479,001,600 permutations appear, by rotation class | 3 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | 2 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | 3 s |
Download
Download Detour (.detour) 41.5 kB, or 522.7 MB decoded
# check it yourself
detour decode W-0051.detour - | tr -d '\n' | shasum -a 256
tar xzf checkers-rs-source.tar.gz && cd checkers-rs && cargo build --release --locked
./target/release/classcheck 12 ../W-0051.detour 522745531
./target/release/bitmapcheck 12 ../W-0051.detour 522745531
./target/release/wordhash 12 ../W-0051.detour 522745531
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 = 12 and sync exponent 0. The file has 4,904,455 tokens: 1 START, 1 literal of 1 byte in all, and 4,904,453 deviations. Deviations by weight, from 1 to 12: 169,346 · 1,354,738 · 3,379,998 · 79 · 82 · 103 · 28 · 20 · 37 · 12 · 9 · 1.