{
  "id": "1505.04458",
  "version": "v1",
  "published": "2015-05-17T21:21:03.000Z",
  "updated": "2015-05-17T21:21:03.000Z",
  "title": "Combinatorial Hopf Algebras of Simplicial Complexes",
  "authors": [
    "Carolina Benedetti",
    "Joshua Hallam",
    "John Machacek"
  ],
  "comment": "An extended abstract version of this paper will appear in the proceedings of FPSAC '15. Comments are welcome",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider a Hopf algebra of simplicial complexes and provide a cancellation-free formula for its antipode. We then obtain a family of combinatorial Hopf algebras by defining a family of characters on this Hopf algebra. The characters of these combinatorial Hopf algebras give rise to symmetric functions that encode information about colorings of simplicial complexes and their $f$-vectors. We also use characters to give a generalization of Stanley's $(-1)$-color theorem. A $q$-analog version of this family of characters is also studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-17T21:21:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16T30",
      "05E05",
      "05E45"
    ],
    "keywords": [
      "combinatorial hopf algebras",
      "simplicial complexes",
      "characters",
      "cancellation-free formula",
      "symmetric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504458B"
    }
  }
}