{
  "id": "2207.06054",
  "version": "v1",
  "published": "2022-07-13T08:57:38.000Z",
  "updated": "2022-07-13T08:57:38.000Z",
  "title": "Further results on the divisibility of $q$-trinomial coefficients",
  "authors": [
    "Ji-Cai Liu",
    "Wei-Wei Qi"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We study divisibility for the $q$-trinomial coefficients $\\tau_0(n,m,q)$, $T_0(n,m,q)$ and $T_1(n,m,q)$, which were first introduced by Andrews and Baxter. In particular, we completely determine $\\tau_0(an,bn,q)$, $T_0(an,bn,q)$ and $T_1(an,bn,q)$ modulo the square of the cyclotomic polynomial $\\Phi_n(q)$ for $(a,b)=(m,m-1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-13T08:57:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11B65",
      "13A05",
      "05A10"
    ],
    "keywords": [
      "trinomial coefficients",
      "study divisibility",
      "cyclotomic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}