{
  "id": "2008.06045",
  "version": "v1",
  "published": "2020-08-13T17:59:02.000Z",
  "updated": "2020-08-13T17:59:02.000Z",
  "title": "Rota's Basis Conjecture holds asymptotically",
  "authors": [
    "Alexey Pokrovskiy"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Rota's Basis Conjecture is a well known problem from matroid theory, that states that for any collection of $n$ bases in a rank $n$ matroid, it is possible to decompose all the elements into $n$ disjoint rainbow bases. Here an asymptotic version of this is proved. We show that it is possible to find $n-o(n)$ disjoint rainbow independent sets of size $n-o(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-13T17:59:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05D15",
      "G.2.1"
    ],
    "keywords": [
      "rotas basis conjecture holds",
      "disjoint rainbow independent sets",
      "disjoint rainbow bases",
      "asymptotic version",
      "matroid theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}