{
  "id": "math/0402324",
  "version": "v1",
  "published": "2004-02-19T21:06:11.000Z",
  "updated": "2004-02-19T21:06:11.000Z",
  "title": "Generalized de Bruijn Cycles",
  "authors": [
    "Joshua N. Cooper",
    "Ronald L. Graham"
  ],
  "comment": "18 pages, 0 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-19T21:06:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94A55",
      "05C70"
    ],
    "keywords": [
      "bruijn cycles",
      "integers modulo",
      "word appears",
      "definition generalizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2324C"
    }
  }
}