W-0089

A superpermutation on 13 symbols, found by Jay Pantone. It beat the previous record W-0088 by 63 letters and was the record on Nov 9, 2026. The next record W-0092 beat it by 85 letters.

Length: 6,747,801,713
Repeated permutations: 1,797,379
Received: Nov 9, 202603:00:48 UTC

Begins

0123456789ABC0123456789AB0C123456789AB01C23456789AB012C3456789AB0123C456789AB01234C56789AB012345C6789AB0123456C789AB0123…

Windows

	6,747,801,701	windows of 13 consecutive letters
=	6,227,020,800	distinct permutations
+	1,797,379	repeated permutations
+	518,983,522	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	11,695,158
4	3,918
5	1,497
6	1,203
7	350
8	1,372
9	452
10	668
11	102
12	120
13	15

How it was found

From the submitter

This word starts from Jakub Halfar's 6,747,801,798-letter word. In fourteen of his blocks I traded rows so that each block frees four trails, and moved those trails to one common insertion point, which saved 22 letters. I then cut the word at every step of weight 5 or more. No permutation window crosses those cuts, so the pieces can go in any order. Gurobi found the order with the most overlap between neighboring pieces, which saved 63 letters more than the original order.

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Learn about the Detour file format

Download Detour (.detour) 221.5 kB, or 6.7 GB decoded