{
  "id": "math/0411557",
  "version": "v2",
  "published": "2004-11-24T17:25:12.000Z",
  "updated": "2004-12-13T13:37:00.000Z",
  "title": "The number of matroids on a finite set",
  "authors": [
    "W. M. B. Dukes"
  ],
  "comment": "10 pages; revised proofs and corrected typos",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we highlight some enumerative results concerning matroids of low rank and prove the tail-ends of various sequences involving the number of matroids on a finite set to be log-convex. We give a recursion for a new, slightly improved, lower bound on the number of rank-$r$ matroids on $n$ elements when $n=2^m-1$. We also prove an adjacent result showing the point-lines-planes conjecture to be true if and only if it is true for a special subcollection of matroids. Two new tables are also presented, giving the number of paving matroids on at most eight elements.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-12-13T13:37:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35"
    ],
    "keywords": [
      "finite set",
      "low rank",
      "enumerative results concerning matroids",
      "lower bound",
      "point-lines-planes conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11557D"
    }
  }
}