The October last year (2018), mathematician Robin Houston tweeted regarding an ongoing problem in Combinatorics, directing attention towards a post on 4Chan,a message board for anime enthusiasts, from 2011.

“The Melancholy of Haruhi Suzumiya”, an anime based on a series of novels, had aired on television in 2006. The first season, containing fourteen episodes, gave rise to multiple extensive debates, having featured time travel and various other philosophical concepts. Be that as it may, the post under consideration featured a different problem altogether. In its initial release, the show was aired in a non-chronological order and subsequently in a different order, when it was released on DVD. This sparked a debate in the fandom about the correct order to watch the show in. Amidst the discussion, someone asked how many episodes one would have to watch if they wanted to watch all possible orders of the show in one go. Within an hour, someone anonymously posted a lower bound for the number with a rough proof. That anonymous post is currently one of the most notable and elegant pieces of literature in the Minimal Superpermutation Problem.

The Minimal Superpermutation Problem tries to find the shortest string of characters that contains all permutations for n objects.

For example, the superpermutation for three objects would be

123121321

Notice that all six permutations can be isolated as subgroups from the string.

(123)121321 1(231)21321

12(312)1321 1231(213)21

12312(132)1 123121(321)

The problem had started to go cold after 25 years of slow progress when interest was restored after Robin Houston accidentally discovered the shortest known superpermutation for n=6 (872 characters in length) one night, proving false the conjecture that the length of the minimal superpermutation is which placed the length of the minimal superpermutation for the same at 873 characters.

The discovery inspired science fiction writer Greg Egan, formerly a mathematics major student, to work on an upper bound for the length of a minimal superpermutation. He announced his result in a couple of days.

All this while, the 4Chan post had been sitting undiscovered for nearly seven years. When discovered, it attracted many articles and videos and a paper with the lead author as “Anonymous 4Chan Poster” Earlier this year, one of the aforementioned videos helped advance the problem even further after “Charlie Vane” posted a previously unknown superpermutation for n=7, 5907 characters in length, shorter than any other known, in the comments on YouTube.

Within a week of the comment, Greg Egan announced another superpermutation for n=7 that was one character shorter than the one mentioned above. However, to keep up with the trend of peculiar findings and announcements, the superpermutation was announced as a music composition “5906”, there being seven letters in the musical octaves. That brings us up to speed with the progress of the Minimal Superpermutation Problem where teams of mathematicians, amateur and professional, continue to work to find superpermutations that haven’t already been found because the numbers exist and have always existed whether we look at them or not but only when we notice them do they become important. L