{
  "id": "2311.05340",
  "version": "v1",
  "published": "2023-11-09T13:08:21.000Z",
  "updated": "2023-11-09T13:08:21.000Z",
  "title": "Quotient of Special Classes of Positroids",
  "authors": [
    "Zhixing Chen",
    "Yumou Fei",
    "Jiyang Gao",
    "Yuxuan Sun",
    "Yuchong Zhang"
  ],
  "comment": "33 pages, 12 figures; This research was carried out as part of the PACE program in the summer of 2023 at Peking University, Beijing; Comments very welcome",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we give a complete characterization of rank $k-1$ positroids that are quotients of the uniform matroid $U_{k,n}$, completing a partial result by Bendetti-Chavez-Jim\\'enez. Furthermore, we show that any pair of positroid quotient with adjacent ranks are related by a cyclic shift on their decorated permutations. We also use the concept of conecklace to give a full characterization of lattice path matroid (LPM) quotient pairs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-09T13:08:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35"
    ],
    "keywords": [
      "special classes",
      "lattice path matroid",
      "complete characterization",
      "uniform matroid",
      "full characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}