{
  "id": "2301.08933",
  "version": "v1",
  "published": "2023-01-21T10:40:46.000Z",
  "updated": "2023-01-21T10:40:46.000Z",
  "title": "A combinatorial formula for LLT cumulants of melting lollipops in terms of spanning trees",
  "authors": [
    "Maciej Kowalski"
  ],
  "comment": "An extended abstract of this work with fewer results and a different title is available at arXiv:2011.15080v2",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove a combinatorial formula for LLT cumulants of melting lollipops as a positive combination of LLT polynomials indexed by spanning trees. The result gives an affirmative answer to a general positivity question for this class of unicellular LLT cumulants, and gives an independent proof of their Schur-positivity. In the special case of the complete graph, we also express the formula in terms of parking functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-21T10:40:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial formula",
      "melting lollipops",
      "spanning trees",
      "unicellular llt cumulants",
      "general positivity question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}