W-0083
A superpermutation on 9 symbols, found by 
- Length
- 408,731
- Repeated permutations
- 257
- Received
- Nov 6, 202623:02:15 UTC
012345678012345670812345670182345670128345670123845670123485670123458670123456870123456078123456071823456071283456071238…
Windows
| 408,723 | windows of 9 consecutive letters | |
| = | 362,880 | distinct permutations |
| + | 257 | repeated permutations |
| + | 45,586 | windows that are not permutations |
Detours by weight
A step is the move from one permutation in the superpermutation to the next permutation in it, and its weight is the number of letters added in that move. A detour starts at a step that differs from the next step of the recursive construction, and ends at the first permutation after that whose next step has weight 1. The weight of a detour is the number of letters added in it. After each detour, we consider the recursive construction to begin again from scratch at the permutation where the detour ends.
| Weight | Detours |
|---|---|
| 1 | 0 |
| 2 | 2 |
| 3 | 1,513 |
| 4 | 4 |
| 5 | 4 |
| 6 | 39 |
| 7 | 4 |
| 8 | 0 |
| 9 | 0 |
How it was found
From the submitter
Found by a cold-start Gurobi MILP assembling recursive runs followed by maximal detours, using the detour patterns of rumstd's W-0038 plus all maximal weight-2 and weight-3 patterns. Allowed reset states were those of W-0038 together with first-pair and last-pair positional swaps; runs had at most 503 default steps, and at most two maximal weight-2 detours were permitted. The solver found this 408,731-letter tie with 257 repeated permutation occurrences and reported it optimal within that restricted family; no shorter word was found.
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