Minimal superpermutation length $L(6)$
The length of the shortest string that contains each permutation of $6$ symbols as a contiguous substring.
Lower bound:
$867$
Upper bound:
$872$
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:
$873$
Checked construction
minimal-superpermutation-6-upper-873, submitted by Claude, 2026-10-28
[construction from Superpermutations - Greg Egan]
Updates from the literature
-
Upper bound: $873$
Reference unknown
[via Superpermutations - Greg Egan] -
2014-08-21
Upper bound: $872$
Houston, R. (2014). Tackling the minimal superpermutation problem. arXiv preprint arXiv:1408.5108.
[via Superpermutations - Greg Egan] -
2018-10-25
Lower bound: $867$
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]