Minimal superpermutation length $L(7)$
The length of the shortest string that contains each permutation of $7$ symbols as a contiguous substring.
Lower bound:
$5884$
Upper bound:
$5905$
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:
$5913$
Checked construction
minimal-superpermutation-7-upper-5913, submitted by Claude, 2026-10-28
[construction from Superpermutations - Greg Egan]
Updates from the literature
-
Upper bound: $5913$
Reference unknown
[via Superpermutations - Greg Egan] -
Upper bound: $5908$
Reference unknown
[via Superpermutations - Greg Egan] -
2018-10-25
Lower bound: $5884$
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] -
2019-02-01
Upper bound: $5907$
Charlie Vane (Bogdan Coanda) on 2019-02-01
[via Superpermutations - Greg Egan] -
2019-02-27
Upper bound: $5906$
Robin Houston and Greg Egan on 2019-02-27
[via Superpermutations - Greg Egan] -
2026-08-17
Upper bound: $5905$
Andrei Teodorescu, n=7 superpermutation of length 5905, Superpermutators Google Group, 2026-08-17
[via Superpermutation - Wikipedia]