Thanks to ``The Melancholy of Haruhi Suzumiya'', a difficult math problem that has not been solved for 25 years may be solved


by

angelene

Mathematicians around the world have expressed their belief that a discussion on the overseas bulletin board 4chan may solve a difficult problem called ` `The Minimal Superpermutation Problem ,'' which has plagued mathematicians for over 25 years. It's attracting interest. The clue to the solution was the viewing order of the episodes of the TV anime ``The Melancholy of Haruhi Suzumiya .''

/sci/ - The Haruhi problem (lower bound) - Science & Math - 4chan
http://boards.4chan.org/sci/thread/10089701/the-haruhi-problem-lower-bound

An anonymous 4chan post could help solve a 25-year-old math mystery - The Verge
https://www.theverge.com/2018/10/24/18019464/4chan-anon-anime-haruhi-math-mystery

The first season of the TV anime ``The Melancholy of Haruhi Suzumiya'' was broadcast in 2006 and consists of 14 episodes. When it was broadcast on TV in 2006, the episodes were aired in a different order than the chronological order of the story, which caused a stir.

The topic of 4chan's anime fan community is often about which episode order to watch The Melancholy of Haruhi Suzumiya. Among them, the question ``If I want to see all the episodes in every possible order, what is the least number of combinations?'' This theme eventually evolved into the ` `Haruhi Problem .'' It rose to prominence and began to be discussed in the mathematics community. This Haruhi problem is a difficult problem called the ``minimum supersubstitution problem'' in the world of mathematics.

'Minimum super-substitution' is a string that includes all combinations. For example, the combination of two elements A and B is 'AB' and 'BA', but the minimum super-substitution of these two characters is 'ABA'. The minimum super-substitution string 'ABA' includes two combinations: 'AB' and 'BA'.



In addition, there are six combinations of the three elements A, B, and C: 'ABC,' 'ACB,' 'BAC,' 'BCA,' 'CAB,' and 'CBA.' And the minimum super-substitution of 3 characters becomes the 9-character string 'ABCABACBA'. The character string 'ABCABACBA' includes all six combinations.



It is thought that the length of this minimum super-substitution string increases exponentially as the number of elements increases. At the time of article creation, the minimum number of characters for super substitution is only known up to 4 elements. The minimum super-substitution problem is to formulate a string of minimal super-substitutions when the number of elements is 'n' and find its proof.

Although this problem was first posed in

a paper in 1993, it remained unresolved for more than 25 years. However, on the 4chan mathematics forum, a proof was posted based on the solution to Haruhi's problem where n is 14, and although it is not in the form of a paper, mathematicians around the world believe that it may be a clue to solving the minimal supersubstitution problem. It attracted attention from.



Jay Pantone, a mathematician at Maquette University, was initially skeptical about the content of this post, but has published a paper (PDF file) based on this post. According to Pantone, to watch all the episodes of ``The Melancholy of Haruhi Suzumiya'', you need to watch at least 93,924,230,411 episodes.

In addition, computer scientist Robin Houston is a mathematician who has been working on the minimum supersubstitution problem for some time, and is excited about the difficult problems in mathematics that are being solved, starting with the Haruhi problem, saying, ``It's an interesting situation.'' Masu.


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