{
  "id": "2406.14244",
  "version": "v1",
  "published": "2024-06-20T12:12:07.000Z",
  "updated": "2024-06-20T12:12:07.000Z",
  "title": "On simple matroids with a unique minimal tropical basis",
  "authors": [
    "Winfried Hochstättler"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this note we characterize tropical bases as sets of circuits that by orthogonality determine the set of cocircuits of a simple matroid. Furthermore, we show that any circuit, which itself is closed, must be contained in any tropical basis. This yields a characterization of simple matroids which have a unique minimal tropical basis, giving a solution for a problem posted in the Matroid Union Blog.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-20T12:12:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35"
    ],
    "keywords": [
      "unique minimal tropical basis",
      "simple matroid",
      "matroid union blog",
      "orthogonality determine",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}