Universal Cycles for Some Combinatorial Objects

<p>A de Bruijn cycle commonly referred to as a universal cycle<em> (u-cycle)</em>, 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<em> n-letter</em> words on a<em> k-letter</em> alphabet for all values of <em>k,n,</em> to prove that we can create de Bruijn cycles for multi-sets using natural encodings and<em> M-Lipschitz n-letter</em> words and the assignment of elements of <em>[n]={1,2,...,n}</em> 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 <em>s</em> and<em> t</em>, where these parameters are suitably restricted.</p>

Name thesis:degree_name

MS (Master of Science)

Level thesis:degree_level

Thesis - unrestricted

Discipline thesis:degree_discipline

Mathematical Sciences

Year dc:date.issued

2013

Author dc:creator

• Campbell, Andre A

• Universal Cycle
• de Bruijn Cycle
• Posets
• Boolean Lattice
• Applied Mathematics
• Physical Sciences and Mathematics

Statement dc:rights

• Copyright by the authors.

Repository record dc:identifier

https://dc.etsu.edu/etd/1130

OAI identifier oai:identifier

oai:dc.etsu.edu:etd-2330