Superpermutation

In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. The smallest superpermutations for n < 5 are 1, 121, 123121321, and 123412314231243121342132413214321, having lengths of 1, 3, 9, and 33 (sequence A180632 in the OEIS). For all n, there is a superpermutation of length 1! + 2! + … + n!, which is minimal only for n < 6.