1 IntroductionA simple example of a universal cycle (U-cycle) is the cyclic string 11101000, whichcontains every 3-letter word on a binary alphabet precisely once. We obtain these wordsby taking substrings of length 3; it is useful to imagine that we are looking at the stringthrough a “window” of length 3, and we shift the window to transition from one word tothe next, allowing the window to wrap if necessary.Universal cycles have been shown to exist for words of any length and for any alphabetsize. (For the special case of a binary alphabet, such strings are also known as de Bruijncycles). The concept easily lends itself to extension, and universal cycles for permutations,partitions, and certain classes of functions are well-studied in the literature (see Chung,Diaconis, Graham for an overview of previous work in the field). In all cases, thedistinguishing feature of a universal cycle is that by shifting a window through a cycli...