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title
Bosker Blog
description
Miscellaneous maundering
image
site name
Bosker Blog
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updated
2025-12-24 03:42:31
raw text
Bosker Blog | Miscellaneous maundering Bosker Blog Miscellaneous maundering Skip to content Home About ← Older posts Superpermutations: lower bound Posted on 2018-10-20 by Robin Houston I wrote about superpermutations here : a superpermutation is a string that has as substrings all the permutations of some set of symbols. For example, there are six permutations of the symbols 1, 2, 3. They are: 123, 132, 213, 231, 312, 321. The string 123121321 has all six of these as substrings – and it’s the shortest string that does, with only one three-character substring that isn’t a permutation: the 121 in the middle. For larger numbers of symbols it’s impossible to do quite so well. For example, there are 24 different permutations of the symbols 1, 2, 3, 4, and the shortest superpermutation is 123412314231243121342132413214321 , which has 33 characters. So there are 30 different four-character substrings, and six of them contain repeated symbols: 1231 , 2312 ; ...
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