Superpermutation Almanac

Bounds

Jakub Halfar's 0*(n-3)! asymptotic upper bound

For large n, S(n) \le n! + (n-1)! + (n-2)! + \left(0 + \varepsilon\right)(n-3)!

Holds for
large n
Announced
Nov 8, 2026
Proof
Lean proof
Coefficient of (n−3)!
0
Points
51.1

By Jakub Halfar.

Evidence

Proof check

kernel-checked

Checked
Nov 8, 2026
Lean version
leanprover/lean4:v4.35.0
Mathlib commit
56a005855ea17e0b0958f73ec801ae140b0a1679
lean4checker
lean4-bundled@eb6cafb7290e8bd5f2937522d8d804f58f02bafc
nanoda
lean4-bundled@eb6cafb7290e8bd5f2937522d8d804f58f02bafc

build 251 s, peak 3.8 GB

Result 1 of batch L-0016, theorem upper_coeff3_zero, checked in attempt 1: AlmanacSolution.lean, line 11.

theorem upper_coeff3_zero : Almanac.AsymptoticUpperAt 3 0

Repository at the checked commit · Repository archive (318.4 kB)

Pantone's 43/80 construction with nested block levels added, built on his Lean library. First in proofs/lean/constant43586371 of my main repository.