{
  "id": "2306.12934",
  "version": "v1",
  "published": "2023-06-22T14:45:06.000Z",
  "updated": "2023-06-22T14:45:06.000Z",
  "title": "On boundedness of zeros of the independence polynomial of tor",
  "authors": [
    "David de Boer",
    "Pjotr Buys",
    "Han Peters",
    "Guus Regts"
  ],
  "comment": "45 pages, 5 figures",
  "categories": [
    "math.CO",
    "cs.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study boundedness of zeros of the independence polynomial of tori for sequences of tori converging to the integer lattice. We prove that zeros are bounded for sequences of balanced tori, but unbounded for sequences of highly unbalanced tori. Here balanced means that the size of the torus is at most exponential in the shortest side length, while highly unbalanced means that the longest side length of the torus is super exponential in the product over the other side lengths cubed. We discuss implications of our results to the existence of efficient algorithms for approximating the independence polynomial on tori.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-22T14:45:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "independence polynomial",
      "shortest side length",
      "longest side length",
      "study boundedness",
      "efficient algorithms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}