W-0043
A superpermutation on 13 symbols, found by Jakub Halfar. It beat the previous record, W-0036, by 8 letters, and was the record for n = 13 from Oct 3 until Oct 4, 2026, when W-0050 was 88 letters shorter.
- Length
- 6,747,918,058
- Repeated occurrences
- 1,693,436
- Announced
- Oct 3, 2026
0123456789ABC0123456789AB0C123456789AB01C23456789AB012C3456789AB0123C456789AB01234C56789AB012345C6789AB0123456C789AB0123…
Windows
| 6,747,918,046 | windows of 13 consecutive letters | |
| = | 6,227,020,800 | distinct permutations, all 13! of them |
| + | 1,693,436 | repeated occurrences of a permutation |
| + | 519,203,810 | windows that are not permutations |
How it was found
Pantone's pieces with the runs reordered as an asymmetric TSP (PR #5).
Checking
Total check time: 1 min 51 s, including preparation but not time in the queue.
| Program | Source | Result | Time |
|---|---|---|---|
| classcheck | 41928cce | all 6,227,020,800 permutations appear, by rotation class | 45 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | 32 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | 34 s |
Download
Download Detour (.detour) 214.7 kB, or 6.7 GB decoded
# check it yourself
detour decode W-0043.detour - | tr -d '\n' | shasum -a 256
tar xzf checkers-rs-source.tar.gz && cd checkers-rs && cargo build --release --locked
./target/release/classcheck 13 ../W-0043.detour 6747918058
./target/release/bitmapcheck 13 ../W-0043.detour 6747918058
./target/release/wordhash 13 ../W-0043.detour 6747918058
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 = 13 and sync exponent 0. The file has 54,099,578 tokens: 1 START, 1 literal of 1 byte in all, and 54,099,576 deviations. Deviations by weight, from 1 to 13: 1,693,436 · 15,240,915 · 37,163,319 · 66 · 173 · 375 · 723 · 231 · 58 · 71 · 101 · 89 · 19.