{
  "id": "2010.00580",
  "version": "v1",
  "published": "2020-10-01T17:53:17.000Z",
  "updated": "2020-10-01T17:53:17.000Z",
  "title": "Ball packings for links",
  "authors": [
    "Jorge Luis Ramírez Alfonsín",
    "Ivan Rasskin"
  ],
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "The ball number of a link $L$, denoted by $ball(L)$, is the minimum number of solid balls needed to realize a necklace representing $L$. In this paper, we show that $ball(L)\\leq 5 cr(L)$ where $cr(L)$ denotes the crossing number of $L$. To this end, we use Lorenz geometry applied to ball packings. Our approach yields to an algorithm to construct explicitly the desired necklace representation of $L$ in the 3-dimensional space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-01T17:53:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C17",
      "57K10"
    ],
    "keywords": [
      "ball packings",
      "minimum number",
      "ball number",
      "lorenz geometry",
      "approach yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}