28 lines
1.9 KiB
Plaintext
28 lines
1.9 KiB
Plaintext
A superpermutation of N different characters is a string consisting of an arrangement of multiple copies of those N different characters in which every permutation of those characters can be found as a substring.
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For example, representing the characters as A..Z, using N=2 we choose to use the first two characters 'AB'. <br>
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The permutations of 'AB' are the two, (i.e. two-factorial), strings: 'AB' and 'BA'.
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A too obvious method of generating a superpermutation is to just join all the permutations together forming 'ABBA'.
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A little thought will produce the shorter (in fact the shortest) superpermutation of 'ABA' - it contains 'AB' at the beginning and contains 'BA' from the middle to the end.
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The "too obvious" method of creation generates a string of length N!*N. Using this as a yardstick, the task is to investigate other methods of generating superpermutations of N from 1-to-7 characters, that never generate larger superpermutations.
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Show descriptions and comparisons of algorithms used here, and select the "Best" algorithm as being the one generating shorter superpermutations.
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The problem of generating the shortest superpermutation for each N ''might'' be NP complete, although the minimal strings for small values of N have been found by brute -force searches.
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{{Template:Strings}}
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;Reference:
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* [http://www.njohnston.ca/2013/04/the-minimal-superpermutation-problem/ The Minimal Superpermutation Problem]. by Nathaniel Johnston.
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* [http://oeis.org/A180632 oeis A180632] gives 0-5 as 0, 1, 3, 9, 33, 153. 6 is thought to be 872.
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* [https://www.youtube.com/watch?v=wJGE4aEWc28 Superpermutations - Numberphile]. A video
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* [https://www.youtube.com/watch?v=OZzIvl1tbPo Superpermutations: the maths problem solved by 4chan - Standupmaths]. A video of recent (2018) mathematical progress.
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* [https://www.youtube.com/watch?v=_tpNuulTeSQ New Superpermutations Discovered!] Standupmaths & Numberphile.
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<br><br>
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