# Does the principle of De Bruijn sequences extend to non-repeating combinations?

The basic principle of the De Bruijn sequence is that for an alphabet of $k$ letters all combinations of $n$-letter words can be found in a sequence of length $k^n$ letters. For example, given the possibility of any ATM pin containing 4 digits (0-9), there is a sequence of $10^4=10000$ digits which contains every possible pin. The length of the De Bruijn sequence is the same as the number of permutations of the letters.

The question is whether this principle extends to words in which the letters are not allowed to repeat. For example, mechanical door combinations do allow the code to repeat the same digit. Imagine a 5-digit mechanical door lock with buttons numbered 1,2,3,4,5. The code is 4-digits long and digits may not be repeated, so there are $5x4x3x2 = 120$ possible combinations.

Does that imply that there is a 120-digit De Bruijn sequence which contains all possible codes for the mechanical lock?