Universal Cycles for Some Combinatorial Objects
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 alp...
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| Format: | Others |
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Digital Commons @ East Tennessee State University
2013
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| Online Access: | https://dc.etsu.edu/etd/1130 https://dc.etsu.edu/cgi/viewcontent.cgi?article=2330&context=etd |
| Summary: | 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. |
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