{
  "id": "2402.11979",
  "version": "v2",
  "published": "2024-02-19T09:26:13.000Z",
  "updated": "2025-01-29T12:52:39.000Z",
  "title": "On a q-analogue of the Zeta polynomial of posets",
  "authors": [
    "Frédéric Chapoton"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a q-analogue of the classical Zeta polynomial of finite partially ordered sets, as a polynomial in one variable x with coefficients depending on the indeterminate q. We prove some properties of this polynomial invariant, including its behaviour with respect to duality, product and disjoint union. The leading term is a q-analogue of the number of maximal chains, but not always with non-negative coefficients. The value at q=0 turns out to be essentially the characteristic polynomial.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-01-29T12:52:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "q-analogue",
      "maximal chains",
      "classical zeta polynomial",
      "disjoint union",
      "finite partially ordered sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}