{
  "id": "1803.08824",
  "version": "v3",
  "published": "2018-03-23T14:58:07.000Z",
  "updated": "2019-07-09T13:00:11.000Z",
  "title": "The kernel of chromatic quasisymmetric functions on graphs and hypergraphic polytopes",
  "authors": [
    "Raul Penaguiao"
  ],
  "comment": "40 pages, 4 figures, this is the longer version",
  "categories": [
    "math.CO",
    "math.RA"
  ],
  "abstract": "We study the chromatic symmetric function on graphs, and show that its kernel is spanned by the modular relations. We generalize this result to the chromatic quasisymmetric function on hypergraphic polytopes, a family of generalized permutahedra. We use this description of the kernel of the chromatic symmetric function to find other graph invariants that may help us tackle the tree conjecture.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2019-07-09T13:00:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05"
    ],
    "keywords": [
      "chromatic quasisymmetric function",
      "hypergraphic polytopes",
      "chromatic symmetric function",
      "modular relations",
      "graph invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}