W-0008
A superpermutation on 6 symbols, found by Robin Houston. It beat the previous record, W-0005, by 1 letter, and is the record for n = 6.
- Length
- 872
- Repeated occurrences
- 0
- Announced
- Aug 21, 2014
012345012340512340152340125340215340251340253140253410253401235401230451230415230412530412350412305412301452301425301423…
Windows
| 867 | windows of 6 consecutive letters | |
| = | 720 | distinct permutations, all 6! of them |
| + | 0 | repeated occurrences of a permutation |
| + | 147 | windows that are not permutations |
How it was found
Found by running the LKH travelling-salesman solver on the n = 6 overlap graph; the first superpermutation shorter than 1! + ... + n!.
Checking
| Program | Source | Result | Time |
|---|---|---|---|
| permcheck | c46d3654 | all 720 permutations appear | under 1 s |
| literal_check | f4687121 | agrees on coverage | under 1 s |
Download
Download Detour (.detour) 220 bytes, or 872 bytes decoded
Download text (.txt) 872 bytes
# check it yourself
detour decode W-0008.detour - | tr -d '\n' | shasum -a 256
tar xzf checkers-rs-source.tar.gz && cd checkers-rs && cargo build --release --locked
./target/release/classcheck 6 ../W-0008.detour 872
./target/release/bitmapcheck 6 ../W-0008.detour 872
./target/release/wordhash 6 ../W-0008.detour 872
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 = 6 and sync exponent 0. The file has 128 tokens: 1 START, 1 literal of 1 byte in all, and 126 deviations. Deviations by weight, from 1 to 6: 0 · 126 · 0 · 0 · 0 · 0.