De Bruijn sequences are cyclic sequences characterised by the property that every possible subsequence of a given length over a fixed alphabet appears exactly once. Their study intertwines with ...

For example, the subsequence AAAA can occur up to 17 times in a sequence of length 20 (which would happen if the sequence were composed solely of A's), but the subsequence ACGT cannot occur more than ...

The selected sequence must increase. The problem is to maximize the expected length of the selected sequence. We demonstrate decision policies which approach optimality when the number of observations ...