Generalized de Bruijn Cycles
| dc.creator | Cooper, Joshua N. | |
| dc.creator | Graham, Ronald L. | |
| dc.date | 2004-02-19 | |
| dc.date.accessioned | 2026-07-07T05:05:36Z | |
| dc.date.available | 2026-07-07T05:05:36Z | |
| dc.description | 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. | |
| dc.description | 18 pages, 0 figures | |
| dc.identifier | https://arxiv.org/abs/math/0402324 | |
| dc.identifier | http://arxiv.org/abs/math/0402324 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70226 | |
| dc.subject | Combinatorics | |
| dc.subject | 94A55; 05C70 | |
| dc.title | Generalized de Bruijn Cycles | |
| dc.type | text |