{
  "id": "1909.04462",
  "version": "v1",
  "published": "2019-09-10T13:15:33.000Z",
  "updated": "2019-09-10T13:15:33.000Z",
  "title": "Lower bounds for periods of Ducci sequences",
  "authors": [
    "Florian Breuer",
    "Igor E. Shparlinski"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "A Ducci sequence is a sequence of integer $n$-tuples obtained by iterating the map \\[ D : (a_1, a_2, \\ldots, a_n) \\mapsto \\big(|a_1-a_2|,|a_2-a_3|,\\ldots,|a_n-a_1|\\big). \\] Such a sequence is eventually periodic and we denote by $P(n)$ the maximal period of such sequences for given $n$. We prove lower bounds for $P(n)$ by counting certain partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-10T13:15:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B83",
      "11P83",
      "11T30"
    ],
    "keywords": [
      "ducci sequence",
      "lower bounds",
      "maximal period",
      "partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}