{
  "id": "2311.01397",
  "version": "v1",
  "published": "2023-11-02T17:04:06.000Z",
  "updated": "2023-11-02T17:04:06.000Z",
  "title": "Schubert matroids, Delannoy paths, and Speyer's invariant",
  "authors": [
    "Luis Ferroni"
  ],
  "comment": "20 pages. 1 ancillary file. To appear in Combinatorial Theory",
  "categories": [
    "math.CO"
  ],
  "abstract": "We provide a combinatorial way of computing Speyer's $g$-polynomial on arbitrary Schubert matroids via the enumeration of certain Delannoy paths. We define a new statistic of a basis in a matroid, and express the $g$-polynomial of a Schubert matroid in terms of it and internal and external activities. Some surprising positivity properties of the $g$-polynomial of Schubert matroids are deduced from our expression. Finally, we combine our formulas with a fundamental result of Derksen and Fink to provide an algorithm for computing the $g$-polynomial of an arbitrary matroid.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-02T17:04:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "delannoy paths",
      "speyers invariant",
      "polynomial",
      "arbitrary schubert matroids",
      "arbitrary matroid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}