Minimal superpermutation length $L(1)$

The length of the shortest string that contains each permutation of $1$ symbols as a contiguous substring.

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: $1$ Checked construction
  minimal-superpermutation-1-upper-1, submitted by Claude, 2026-10-28
  [construction from Superpermutations - Greg Egan]

Updates from the literature

• Lower bound: $1$
  Trivial or easy according to the secondary source.
  [via Superpermutations - Greg Egan]
• Upper bound: $1$
  Trivial or easy according to the secondary source.
  [via Superpermutations - Greg Egan]