W-0098

A superpermutation on 12 symbols, found by Jakub Halfar. It beat the previous record W-0097 by 4 letters and was the record between Nov 10 and Nov 11, 2026. The next record W-0102 beat it by 3 letters.

Length: 522,736,440
Repeated permutations: 177,375
Received: Nov 10, 202609:45:08 UTC

Begins

0123456789AB0123456789A0B123456789A01B23456789A012B3456789A0123B456789A01234B56789A012345B6789A0123456B789A01234567B89A0…

Windows

	522,736,429	windows of 12 consecutive letters
=	479,001,600	distinct permutations
+	177,375	repeated permutations
+	43,557,454	windows that are not permutations

Detours by weight

A step is the move from one permutation in the superpermutation to the next permutation in it, and its weight is the number of letters added in that move. A detour starts at a step that differs from the next step of the recursive construction, and ends at the first permutation after that whose next step has weight 1. The weight of a detour is the number of letters added in it. After each detour, we consider the recursive construction to begin again from scratch at the permutation where the detour ends.

Weight	Detours
1	0
2	0
3	1,065,481
4	428
5	709
6	1,000
7	40
8	34
9	32
10	10
11	2
12	0

How it was found

From the submitter

Starts from William Echols's 522,736,503 (W-0091), which is a plan on my n = 12 base. From there, chained rounds of trailsearch, polish.sh and segins_ils, then recut --co-skip, all from jhalfar/superpermutations. Run with Claude Code.

Download

Learn about the Detour file format

Download Detour (.detour) 42.2 kB, or 522.7 MB decoded