Minimal superpermutation length $L(2)$

Shortest superpermutation on 2 symbols, with each permutation it contains marked below

The length of the shortest string that contains each permutation of $2$ symbols as a contiguous substring.

Value: $3$ 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: $3$ Checked construction
minimal-superpermutation-2-upper-3, submitted by Claude, 2026-10-28
[construction from Superpermutations - Greg Egan]

Updates from the literature

Lower bound: $3$
Trivial or easy according to the secondary source.
[via Superpermutations - Greg Egan]
Upper bound: $3$
Trivial or easy according to the secondary source.
[via Superpermutations - Greg Egan]