W-0062
A superpermutation on 10 symbols, found by Jakub Halfar. It beat the previous record, W-0040, by 18 letters, and is the record for n = 10.
- Length
- 4,034,855
- Repeated occurrences
- 2,349
- Announced
- Oct 6, 2026
012345678901234567809123456780192345678012934567801239456780123495678012345967801234569780123456798012345670891234567081…
Windows
| 4,034,846 | windows of 10 consecutive letters | |
| = | 3,628,800 | distinct permutations, all 10! of them |
| + | 2,349 | repeated occurrences of a permutation |
| + | 403,697 | windows that are not permutations |
How it was found
rumstd's word structure on a new selection with 350 closed trails instead of 364; the Lean kernel checks HasWord 10 4034855 in Halfar's library.
Checking
Total check time: 1 s, including preparation but not time in the queue.
| Program | Source | Result | Time |
|---|---|---|---|
| classcheck | 41928cce | all 3,628,800 permutations appear, by rotation class | under 1 s |
| bitmapcheck | 288b3f67 | agrees, by Lehmer rank | under 1 s |
| wordhash | 94925fe4 | the SHA-256 of the word and of its mirror | under 1 s |
Download
Download Detour (.detour) 1.9 kB, or 4.0 MB decoded
# check it yourself
detour decode W-0062.detour - | tr -d '\n' | shasum -a 256
tar xzf checkers-rs-source.tar.gz && cd checkers-rs && cargo build --release --locked
./target/release/classcheck 10 ../W-0062.detour 4034855
./target/release/bitmapcheck 10 ../W-0062.detour 4034855
./target/release/wordhash 10 ../W-0062.detour 4034855
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 = 10 and sync exponent 0. The file has 54,096 tokens: 1 START, 1 literal of 1 byte in all, and 54,094 deviations. Deviations by weight, from 1 to 10: 2,349 · 14,094 · 37,584 · 18 · 3 · 5 · 38 · 2 · 1 · 0.