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A de Bruijn cycle is a cyclic listing of length A, of a collection of Acombinatorial objects, so that each object appears exactly once as a set ofconsecutive elements in the cycle. In this paper, we show the power of deBruijn's original theorem, namely that the cycles bearing his name exist forn-letter words on a k-letter alphabet for all values of k,n, to prove that wecan create de Bruijn cycles for the assignment of elements of [n]={1,2,....,n}to the sets in any labeled subposet of the Boolean lattice; de Bruijn's theoremcorresponds to the case when the subposet in question consists of a singleground element. The landmark work of Chung, Diaconis, and Graham extended theagenda of finding de Bruijn cycles to possibly the next most natural set ofcombinatorial objects, namely k-subsets of [n]. In this area, importantcontributions have been those of Hurlbert and Rudoy. Here we follow thedirection of Blanca and Godbole, who proved that, in a suitable encoding, deBruijn cycles can be created for the subsets of [n$ of size in the interval[s,t]; 0<=s<t<=n$. In this paper we generalize this result to exhibit existenceof de Bruijn cycles for words with weight between s and t, where theseparameters are suitably restricted.

Contributions to the theory of de Bruijn cycles