{
  "id": "1210.0626",
  "version": "v1",
  "published": "2012-10-02T01:11:23.000Z",
  "updated": "2012-10-02T01:11:23.000Z",
  "title": "Semidirect sums of matroids",
  "authors": [
    "Joseph E. Bonin",
    "Joseph P. S. Kung"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For matroids M and N on disjoint sets S and T, a semidirect sum of M and N is a matroid K on the union of S and T that, like the direct sum and the free product, has the restriction of K to S equal to M and the contraction of K to T equal to N. We abstract a matrix construction to get a general matroid construction: the matroid union of any rank-preserving extension of M on the union of S and T with the direct sum of N and the rank-0 matroid on S is a semidirect sum of M and N. We study principal sums in depth; these are such matroid unions where the extension of M has each element of T added either as a loop or freely on a fixed flat of M. A second construction of semidirect sums, defined by a Higgs lift, also specializes to principal sums. We also explore what can be deduced if M and N, or certain of their semidirect sums, are transversal or fundamental transversal matroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-02T01:11:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "05B20",
      "05C35",
      "05D99",
      "06C10",
      "51M04"
    ],
    "keywords": [
      "semidirect sum",
      "matroid union",
      "fundamental transversal matroids",
      "general matroid construction",
      "study principal sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.0626B"
    }
  }
}