Minimal superpermutation length $L(8)$
The length of the shortest string that contains each permutation of $8$ symbols as a contiguous substring.
Lower bound:
$46085$
(46,085)
Upper bound:
$46205$
(46,205)
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
- Lower bound: None yet
- Upper bound: None yet
Updates from the literature
-
Upper bound: $46233$
(46,233)
Reference unknown
[via Superpermutations - Greg Egan] -
Upper bound: $46205$
(46,205)
Reference unknown
[via Superpermutations - Greg Egan] -
2018-10-25
Lower bound: $46085$
(46,085)
Anonymous 4chan poster, R. Houston, J. Pantone and V. Vatter. A lower bound on the length of the shortest superpattern (2018).
[via Superpermutations - Greg Egan]