2004/02/19 by Joshua Cooper, Joshua N. Cooper, Ronald L. Graham +3
Computer Science · Engineering · Mathematics · #05C70 #94A55 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO #msc:05C70 #msc:94A55
paper · pdf · doi:10.48550/arxiv.math/0402324
18 pages, 0 figures
arxiv created 2004/02/19 · openalex publication_date 2004/02/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 qn 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.