We present sufficient conditions for when an ordering of universal cycles α 1 , α 2 , . . . , α m for disjoint sets S 1 , S 2 , . . . , S m can be concatenated together to obtain a universal cycle for S = S 1 ∪ S 2 ∪ ⋯ ∪ S m . When S is the set of all k-ary strings of length n, the result of such a successful construction is a de Bruijn sequence. Our conditions are applied to generalize two previously known de Bruijn sequence constructions and then they are applied to develop three new de Bruijn sequence constructions. *
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