Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2013
Committee Chair or Co-Chairs
Anant Godbole
Committee Members
Rick Norwood, Debra Knisley
Abstract
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.
Document Type
Thesis - unrestricted
Recommended Citation
Campbell, Andre A., "Universal Cycles for Some Combinatorial Objects" (2013). Electronic Theses and Dissertations. Paper 1130. https://dc.etsu.edu/etd/1130
Copyright
Copyright by the authors.