{
  "id": "2408.15506",
  "version": "v1",
  "published": "2024-08-28T03:29:07.000Z",
  "updated": "2024-08-28T03:29:07.000Z",
  "title": "Analytic properties of Speyer's $g$-polynomial of uniform matroids",
  "authors": [
    "Rong Zhang",
    "James Jing Yu Zhao"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $U_{n,d}$ denote the uniform matroid of rank $d$ on $n$ elements. We obtain some recurrence relations satisfied by Speyer's $g$-polynomials $g_{U_{n,d}}(t)$ of $U_{n,d}$. Based on these recurrence relations, we prove that the polynomial $g_{U_{n,d}}(t)$ has only real zeros for any $n-1\\geq d\\geq 1$. Furthermore, we show that the coefficient of $g_{U_{n,[n/2]}}(t)$ is asymptotically normal by local and central limit theorems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-28T03:29:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B35",
      "26C10",
      "60F05",
      "62E20"
    ],
    "keywords": [
      "uniform matroid",
      "analytic properties",
      "polynomial",
      "recurrence relations",
      "central limit theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}