{
  "id": "1202.2247",
  "version": "v1",
  "published": "2012-02-10T12:40:44.000Z",
  "updated": "2012-02-10T12:40:44.000Z",
  "title": "Unlabeled equivalence for matroids representable over finite fields",
  "authors": [
    "S. R. Kingan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We present a new type of equivalence for representable matroids that uses the automorphisms of the underlying matroid. Two $r\\times n$ matrices $A$ and $A'$ representing the same matroid $M$ over a field $F$ are {\\it geometrically equivalent representations} of $M$ if one can be obtained from the other by elementary row operations, column scaling, and column permutations. Using geometric equivalence, we give a method for exhaustively generating non-isomorphic matroids representable over a finite field $GF(q)$, where $q$ is a power of a prime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-10T12:40:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite field",
      "unlabeled equivalence",
      "generating non-isomorphic matroids representable",
      "elementary row operations",
      "column permutations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.2247K"
    }
  }
}