I have a combinatorial problem that I think is related to sequences over an alphabet.
The situation is the following: I have an alphabet of n symbols and I want to look at sequences that contain each symbol at most m times.
For which m and n exists a sequence s such that for each subset of the n symbols, there exists a substring of s containing exactly these symbols?
Example: 1) If I have 3 symbols A,B,C and K=2, there exists such a sequence: ABCA, which contains (apart from the singleton subsets and the whole set) all subsets consisting of two symbols as substrings. 2) If K is unlimited, there exists such a sequence for each n since I can just spell out all subsets. The length of this string is exponential in n.
Has anyone encountered a problem like this? I'd really appreciate pointers to related theories.