{
  "id": "1011.4269",
  "version": "v1",
  "published": "2010-11-18T20:03:06.000Z",
  "updated": "2010-11-18T20:03:06.000Z",
  "title": "Axioms for the g-vector of general convex polytopes",
  "authors": [
    "Jonathan Fine"
  ],
  "comment": "LaTeX2e. 10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "McMullen's g-vector is important for simple convex polytopes. This paper postulates axioms for its extension to general convex polytopes. It also conjectures that, for each dimension d, a stated finite calculation gives the formula for the extended g-vector. This calculation is done by computer for d=5 and the results analysed. The conjectures imply new linear inequalities on convex polytope flag vectors. Underlying the axioms is a hypothesised higher-order homology extension to middle perversity intersection homology (order-zero homology), which measures the failure of lower-order homology to have a ring structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-18T20:03:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52B11",
      "55N33"
    ],
    "keywords": [
      "general convex polytopes",
      "convex polytope flag vectors",
      "middle perversity intersection homology",
      "simple convex polytopes",
      "hypothesised higher-order homology extension"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.4269F"
    }
  }
}