{
  "id": "2411.01128",
  "version": "v1",
  "published": "2024-11-02T04:08:29.000Z",
  "updated": "2024-11-02T04:08:29.000Z",
  "title": "Chromatic polynomial and the $\\mathfrak{so}$ weight system",
  "authors": [
    "Sergei Lando",
    "Zhuoke Yang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In a recent paper by M.Kazarian and the second author, a recurrence for the Lie algebras $\\mathfrak{so}(N)$ weight systems has been suggested; the recurrence allows one to construct the universal $\\mathfrak{so}$ weight system. The construction is based on an extension of the $\\mathfrak{so}$ weight systems to permutations. Another recent paper, by M. Kazarian, N. Kodaneva, and the first author, shows that under the substitution $C_m=xN^{m-1}, m=1,2,\\dots,$ for the Casimir elements $C_m$, the leading term in $N$ of the value of the universal $\\mathfrak{gl}$ weight system becomes the chromatic polynomial of the intersection graph of the chord diagram. In the present paper, we establish a similar result for the universal $\\mathfrak{so}$ weight system. That is, we show that the leading term of the universal $\\mathfrak{so}$ weight system also becomes the chromatic polynomial under a specific substitution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-02T04:08:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weight system",
      "chromatic polynomial",
      "leading term",
      "second author",
      "recurrence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}