The Haruhi Problem

The Haruhi Problem is a math issue or puzzle that may have been solved or aided in solution by an anonymous 4chan post about all the possible permutations of watching Season 1 of The Melancholy of Haruhi Suzumiya anime.

Removed from its relation to the anime, the math puzzle is this: "what is the shortest string containing all permutations of a set of n elements?"