{
  "id": "math/0405535",
  "version": "v2",
  "published": "2004-05-27T23:05:46.000Z",
  "updated": "2005-02-18T17:57:25.000Z",
  "title": "Inequalities for the h- and flag h-vectors of geometric lattices",
  "authors": [
    "Kathryn Nyman",
    "Ed Swartz"
  ],
  "comment": "15 pages, 2 figures. Typos fixed; most notably in Table 1. A note was added regarding a solution to problem 4.6",
  "journal": "Discrete and Computational Geometry, Vol. 32, No. 4, Nov. 2004, pgs 533-548",
  "doi": "10.1007/s00454-004-1137-z",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that the order complex of a geometric lattice has a convex ear decomposition. As a consequence, if D(L) is the order complex of a rank (r+1) geometric lattice L, then for all i \\leq r/2 the h-vector of D(L) satisfies h(i-1) \\leq h(i) and h(i) \\leq h(r-i). We also obtain several inequalities for the flag h-vector of D(L) by analyzing the weak Bruhat order of the symmetric group. As an application, we obtain a zonotopal cd-analogue of the Dowling-Wilson characterization of geometric lattices which minimize Whitney numbers of the second kind. In addition, we are able to give a combinatorial flag h-vector proof of h(i-1) \\leq h(i) when i \\leq (2/7)(r + 5/2).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-02-18T17:57:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "06C10"
    ],
    "keywords": [
      "geometric lattice",
      "inequalities",
      "order complex",
      "combinatorial flag h-vector proof",
      "weak bruhat order"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5535N"
    }
  }
}