Mathematics – Combinatorics
Scientific paper
2004-02-19
Mathematics
Combinatorics
18 pages, 0 figures
Scientific paper
For a set of integers $I$, we define a $q$-ary $I$-cycle to be a assignment of the symbols 1 through $q$ to the integers modulo $q^n$ so that every word appears on some translate of $I$. This definition generalizes that of de Bruijn cycles, and opens up a multitude of questions. We address the existence of such cycles, discuss ``reduced'' cycles (ones in which the all-zeroes string need not appear), and provide general bounds on the shortest sequence which contains all words on some translate of $I$. We also prove a variant on recent results concerning decompositions of complete graphs into cycles and employ it to resolve the case of $|I|=2$ completely.
Cooper Joshua N.
Graham Ronald L.
No associations
LandOfFree
Generalized de Bruijn Cycles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Generalized de Bruijn Cycles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized de Bruijn Cycles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-709272