The shortest circular sequence of length σ^n such that every string of length n on the alphabet a of size σ occurs as a contiguous subrange of the sequence described by a. For example, a de Bruijn sequence of order n = 2 on the alphabet {a, b, c} is given by {a, a, c, b, b, c, c, a, b}. A de Bruijn sequence can be generated in the Wolfram Language using DeBruijnSequence[list, n]. Every de Bruijn sequence corresponds to an Eulerian cycle on a de Bruijn graph. Surprisingly, it turns out that the lexicographic sequence of Lyndon words of lengths divisible by n gives the lexicographically smallest de Bruijn sequence (Ruskey).

de Bruijn graph | Lyndon word