Universal cycles of classes of restricted words

It is well known that Universal cycles (U-cycles) of k -letter words on an n -letter alphabet exist for all k and n . In this paper, we prove that Universal cycles exist for several restricted classes of words, including non-bijections, “equitable” words (under suitable restrictions), ranked permutations, and “passwords”. In each case, proving the connectedness of the underlying de Bruijn digraph is a non-trivial step.