{
  "id": "1202.0038",
  "version": "v2",
  "published": "2012-01-31T21:50:12.000Z",
  "updated": "2012-05-18T05:57:21.000Z",
  "title": "Inequalities between gamma-polynomials of graph-associahedra",
  "authors": [
    "Natalie Aisbett"
  ],
  "comment": "17 pages, 11 figures",
  "journal": "The Electronic Journal of Combinatorics 19, (2012), 2, p36",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove a conjecture of Postnikov, Reiner and Williams by defining a partial order on the set of tree graphs with $n$ vertices that induces inequalities between the $\\gamma$-polynomials of their associated graph-associahedra. The partial order is given by relating trees that can be obtained from one another by operations called tree shifts. We also show that tree shifts lower the $\\gamma$-polynomials of graphs that are not trees, as do the flossing moves of Babson and Reiner.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-18T05:57:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partial order",
      "gamma-polynomials",
      "tree shifts lower",
      "tree graphs",
      "induces inequalities"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.0038A"
    }
  }
}