A de Bruijn cycle commonly referred to as a universal cycle (u-cycle), is a complete and compact listing of a collection of combinatorial objects. In this paper, we show the power of de Bruijn's original theorem, namely that the cycles bearing his name exist for n-letter words on a k-letter alphabet for all values of k,n, to prove that we can create de Bruijn cycles for multi-sets using natural encodings and M-Lipschitz n-letter words and the assignment of elements of [n]={1,2,...,n} to the sets in any labeled subposet of the Boolean lattice; de Bruijn's theorem corresponds to the case when the subposet in question consists of a single ground element. In this paper, we also show that de Bruijn's cycles exist for words with weight between s and t, where these parameters are suitably restricted.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etd-2330 |
| Date | 01 May 2013 |
| Creators | Campbell, Andre A |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
| Rights | Copyright by the authors. |
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