{
  "id": "0712.1560",
  "version": "v1",
  "published": "2007-12-10T19:16:21.000Z",
  "updated": "2007-12-10T19:16:21.000Z",
  "title": "The Lefschetz property for barycentric subdivisions of shellable complexes",
  "authors": [
    "Martina Kubitzke",
    "Eran Nevo"
  ],
  "comment": "16 pages, no figures",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "We show that an 'almost strong Lefschetz' property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a Cohen-Macaulay complex, the $h$-vector is unimodal, peaks in its middle degree (one of them if the dimension of the complex is even), and that its $g$-vector is an $M$-sequence. In particular, the (combinatorial) $g$-conjecture is verified for barycentric subdivisions of homology spheres. In addition, using the above algebraic result, we derive new inequalities on a refinement of the Eulerian statistics on permutations, where permutations are grouped by the number of descents and the image of 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-10T19:16:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F55"
    ],
    "keywords": [
      "barycentric subdivision",
      "lefschetz property",
      "shellable complexes",
      "eulerian statistics",
      "middle degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.1560K"
    }
  }
}