{
  "id": "1601.08199",
  "version": "v1",
  "published": "2016-01-29T17:19:09.000Z",
  "updated": "2016-01-29T17:19:09.000Z",
  "title": "Degree bounds for the toric ideal of a matroid",
  "authors": [
    "Michał Lasoń"
  ],
  "categories": [
    "math.CO",
    "math.AC",
    "math.AG"
  ],
  "abstract": "Describing minimal generating set of a toric ideal, or the minimum degree in which it is generated, is a well-studied and difficult problem. In 1980 White conjectured that the toric ideal of a matroid is generated by quadratic binomials corresponding to symmetric exchanges. In particular, that it is generated in degree $2$. We prove that the toric ideal associated to a matroid of rank $r$ is generated in degree at most $(r+3)!$. As a corollary we obtain that checking if White's conjecture is true for matroids of a fixed rank is a decidable problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-29T17:19:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "13P10",
      "14M25",
      "90C27"
    ],
    "keywords": [
      "toric ideal",
      "degree bounds",
      "whites conjecture",
      "minimal generating set",
      "symmetric exchanges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}