{
  "id": "1906.05848",
  "version": "v1",
  "published": "2019-06-13T17:48:38.000Z",
  "updated": "2019-06-13T17:48:38.000Z",
  "title": "Multivariate polynomials for generalized permutohedra",
  "authors": [
    "Eric Katz",
    "McCabe Olsen"
  ],
  "comment": "16 pages, 6 figures, comments welcome",
  "categories": [
    "math.CO"
  ],
  "abstract": "Using the notion of Mahonian statistic on acyclic posets, we introduce a $q$-analogue of the $h$-polynomial of a simple generalized permutohedron. We focus primarily on the case of nestohedra and on explicit computations for many interesting examples, such as $S_n$-invariant nestohedra, graph associahedra, and Stanley--Pitman polytopes. For the usual (Stasheff) associahedron, our generalization yields an alternative $q$-analogue to the well-studied Narayana numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-13T17:48:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multivariate polynomials",
      "simple generalized permutohedron",
      "acyclic posets",
      "mahonian statistic",
      "invariant nestohedra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}