{
  "id": "math/0606356",
  "version": "v1",
  "published": "2006-06-15T11:44:05.000Z",
  "updated": "2006-06-15T11:44:05.000Z",
  "title": "$f$-Vectors of Barycentric Subdivisions",
  "authors": [
    "Francesco Brenti",
    "Volkmar Welker"
  ],
  "categories": [
    "math.CO",
    "math.AT"
  ],
  "abstract": "For a simplicial complex or more generally Boolean cell complex $\\Delta$ we study the behavior of the $f$- and $h$-vector under barycentric subdivision. We show that if $\\Delta$ has a non-negative $h$-vector then the $h$-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney-Davis conjecture for spheres that are the subdivision of a Boolean cell complex. For a general $(d-1)$-dimensional simplicial complex $\\Delta$ the $h$-polynomial of its $n$-th iterated subdivision shows convergent behavior. More precisely, we show that among the zeros of this $h$-polynomial there is one converging to infinity and the other $d-1$ converge to a set of $d-1$ real numbers which only depends on $d$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-15T11:44:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "barycentric subdivision",
      "boolean cell complex",
      "dimensional simplicial complex",
      "polynomial",
      "strong version"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6356B"
    }
  }
}