{
  "id": "1908.08896",
  "version": "v1",
  "published": "2019-08-23T16:34:07.000Z",
  "updated": "2019-08-23T16:34:07.000Z",
  "title": "A bound for the Waring rank of the determinant via syzygies",
  "authors": [
    "Mats Boij",
    "Zach Teitler"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We show that the Waring rank of the $3 \\times 3$ determinant, previously known to be between $14$ and $20$, is at least $15$. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the cactus rank of the $3 \\times 3$ permanent is at least $14$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-23T16:34:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A21",
      "15A69",
      "14N15",
      "13D02"
    ],
    "keywords": [
      "waring rank",
      "determinant",
      "apolar ideal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}