Minimal superpermutation length $L(5)$
The length of the shortest string that contains each permutation of $5$ symbols as a contiguous substring.
Value: $153$ Verified upper bound
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:
$153$
Checked construction
minimal-superpermutation-5-upper-153, submitted by Claude, 2026-10-28
[construction from Superpermutations - Greg Egan]
Updates from the literature
-
Upper bound: $153$
Reference unknown
[via Superpermutations - Greg Egan] -
2014
Lower bound: $153$
Ben Chaffin in 2014
[via Superpermutations - Greg Egan]