W-0090

A superpermutation on 14 symbols, found by Jay Pantone. It beat the previous record W-0085 by 18,947 letters and has been the record since Nov 9, 2026.

Length: 93,904,785,458
Repeated permutations: 19,714,034
Received: Nov 9, 202603:23:04 UTC

Begins

0123456789ABCD0123456789ABCD1023456789ABCD1203456789ABCD1230456789ABCD1234056789ABCD1234506789ABCD1234560789ABCD12345670…

Windows

	93,904,785,445	windows of 14 consecutive letters
=	87,178,291,200	distinct permutations
+	19,714,034	repeated permutations
+	6,706,780,211	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	212,812
3	138,007,540
4	100,588
5	22,225
6	3,254
7	2,018
8	351
9	287
10	259
11	696
12	182
13	86
14	3

How it was found

From the submitter

This word is built from the selection behind my 926683/1814400 upper bound, not from an earlier word. Its closed trails are joined by splicing rows inside their 13-letter factors. One 13-letter circle for each transport parent joins that parent's eleven completion trails, and 1,136 more 13-letter circles join the parents along the four transports. Each of the 48 remaining sectors keeps its cover of 1,157 eleven-letter circles. This gives 338 pieces. I then cut the word at every step of weight 5 or more, where no permutation window crosses, and put the pieces in the order with the most overlap between neighbors, found with Gurobi and a local search.

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Learn about the Detour file format

Download Detour (.detour) 421.0 kB, or 93.9 GB decoded