Superpermutation Almanac

Back to n = 13

W-0100

A superpermutation on 13 symbols, found by Jay Pantone. It beat the previous record W-0094 by 157 letters and has been the record since Nov 10, 2026.

Length
6,747,801,038
Repeated permutations
1,797,020
Received
Nov 10, 202620:27:39 UTC
Begins 0123456789ABC0123456789AB0C123456789AB01C23456789AB012C3456789AB0123C456789AB01234C56789AB012345C6789AB0123456C789AB0123…

Windows

6,747,801,026windows of 13 consecutive letters
=6,227,020,800distinct permutations
+1,797,020repeated permutations
+518,983,206windows 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.

WeightDetours
10
20
311,695,408
43,093
52,278
61,045
7344
81,247
9434
10562
11106
12148
1311

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. I then alternated Jakub Halfar's trailsearch, which moves and re-cuts trails, with further Gurobi reorderings, which saved 87 more letters. Adding his polish.sh, a set of local searches over where trails are opened and joined, as a third step of the alternation, with its loopscan step allowed far more rounds than its default, saved 588 more letters.

Download

Learn about the Detour file format

Download Detour (.detour) 223.9 kB, or 6.7 GB decoded