{
  "id": "1811.01687",
  "version": "v1",
  "published": "2018-11-05T13:54:31.000Z",
  "updated": "2018-11-05T13:54:31.000Z",
  "title": "Matroid-minor Hopf algebra: a cancellation-free antipode formula and other applications of sign-reversing involutions",
  "authors": [
    "Eric Bucher",
    "Chris Eppolito",
    "Jaiung Jun",
    "Jacob P. Matherne"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we give a cancellation-free antipode formula for the matroid-minor Hopf algebra. We then explore applications of this formula. For example, the cancellation-free formula expresses the antipode of uniform matroids as a sum over certain ordered set partitions. We also prove that all matroids over any hyperfield (in the sense of Baker and Bowler) have cancellation-free antipode formulas; furthermore, the cancellations in the antipode are independent of the hyperfield structure and only depend on the underlying matroid.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-05T13:54:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16T30",
      "05B35"
    ],
    "keywords": [
      "cancellation-free antipode formula",
      "matroid-minor hopf algebra",
      "sign-reversing involutions",
      "applications",
      "cancellation-free formula expresses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}