{
  "id": "1103.0503",
  "version": "v1",
  "published": "2011-03-02T17:55:24.000Z",
  "updated": "2011-03-02T17:55:24.000Z",
  "title": "New Representations of Matroids and Generalizations",
  "authors": [
    "Zur Izhakian",
    "John Rhodes"
  ],
  "comment": "27 pages",
  "categories": [
    "math.CO",
    "math.AC",
    "math.AT",
    "math.RT"
  ],
  "abstract": "We extend the notion of matroid representations by matrices over fields and consider new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This idea of representations is generalized naturally to include also hereditary collections. We show that a matroid that can be directly decomposed as matroids, each of which is representable over a field, has a boolean representation, and more generally that any arbitrary hereditary collection is superboolean-representable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-02T17:55:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B40",
      "05B35",
      "03G05",
      "06G75",
      "55U10"
    ],
    "keywords": [
      "generalizations",
      "arbitrary hereditary collection",
      "finite semirings",
      "matroid representations",
      "boolean representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.0503I"
    }
  }
}